Skip to main content
SpringerLink
Log in

H

  • Chapter
Encyclopaedia of Mathematics

Part of the book series: Encyclopaedia of Mathematics ((ENMA,volume 2))

  • 743 Accesses

Abstract

A Hausdorff space which, under any topological imbedding into an arbitrary Hausdorff space Y, is a closed set in Y. The characteristic property of an H-closed space is that any open covering of the space contains a finite subfamily the closures of the elements of which cover the space. A regular H-closed space is compact. If every closed subspace of a space is H-closed, then the space itself is compact. A theory has been developed for H-closed extensions of Hausdorff spaces.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Aleksandrov, P.S. and Urysohn, P.S.: ‘Mémoire sur les espaces topologiques compacts’, Verh. Akad. Wetensch. Amsterdam 14 (1929).

    Google Scholar 

  2. Iliadis, S.D. and Fomin, S.V.: ‘The method of centred systems in the theory of topological spaces’, Russ. Math. Surveys 21, no. 4 (1966), 37–62. (Uspekhi Mat. Nauk 21, no. 4 (1966), 47-76)

    MathSciNet  MATH  Google Scholar 

  3. Malykhin, V.I. and Ponomarev, V.I.: ‘General topology (set-theoretic trend)’, J. Soviet Math. 7 (1977), 587–653. (Itogi Nauk. i Tekhn. Algebra Topol. Geom. 13 (1975), 149-230)

    Google Scholar 

  4. Porter, J.R. and Woods, R.G.: Extensions and absolutes of Hausdorff spaces, Springer, 1988.

    Google Scholar 

  5. Novikov, S.P.: ‘Homotopy-equivalent smooth manifolds I’, Izv. Akad. Nauk SSSR Ser. Mat. 28, no. 2 (1964), 365–474 (in Russian).

    MathSciNet  Google Scholar 

  6. Milnor, J.: Lectures on the h-cobordism theorem, Princeton Univ. Press, 1965.

    Google Scholar 

  7. Milnor, J.: ‘Whitehead torsion’, Bull. Amer. Math. Soc. 72 (1966), 358–462.

    MathSciNet  MATH  Google Scholar 

  8. Smale, S.: ‘On the structure of manifolds’, Amer. J. Math. 84 (1962), 387–399.

    MathSciNet  MATH  Google Scholar 

  9. Milnor, J.: ‘Sommes des variétés différentiables et structures différentiables des sphères’, Bull. Soc. Math. France 87 (1959), 439–444.

    MathSciNet  MATH  Google Scholar 

  10. Kervaire, M. and Milnor, J.: ‘Groups of homotopy spheres I’, Ann. of Math. (2) 77 (1963), 504–537.

    MathSciNet  MATH  Google Scholar 

  11. Mazur, B.: ‘Relative neighbourhoods and the theorems of Smale’, Ann. of Math. 77 (1963), 232–249.

    MathSciNet  MATH  Google Scholar 

  12. Siebenmann, L.: ‘Disruption of low-dimensional handlebody theory by Rohlin’s theorem’, in Topology of manifolds, Markham, 1969, pp. 57-76.

    Google Scholar 

  13. Kirby, R. and Siebenmann, L.: ‘On the triangulation of manifolds and the Hauptvermutung’, Bull. Amer. Math. Soc. 75 (1969), 742–749.

    MathSciNet  MATH  Google Scholar 

  14. Kervaire, M.: ‘Le théorème de Barden—Mazur—Stallings’, in M. Kervaire, G. de Rham and S. Maumary (eds.): Torsion et type simple d’homotopie, Lecture notes in math., Vol. 48, Springer, 1967, pp. 83-95.

    Google Scholar 

  15. Thom, R.: Les classes caractéristiques de Pontryagin des variétés triangulées, Univ. Nac. Aut. Mexico & UNESCO, 1958, pp. 54-67.

    Google Scholar 

  16. Rourke, C.P. and Sanderson, B.J.: Introduction to piecewise-linear topology, 1972.

    Google Scholar 

  17. Smale, S.: ‘Generalized Poincaré’s conjecture in dimensions greater than four’, Ann. of Math. (2) 74 (1961), 391–406.ai][A1]_Zames, G.: ‘Feedback and complexity, Special plenary lecture addendum’, in lEEE Conf. Decision Control, IEEE, 1976.

    MathSciNet  MATH  Google Scholar 

  18. Zames, G.: ‘Optimal sensitivity and feedback: weighted semi-norms, approximate inverses, and plant invariant schemes’, in Proc. Allerton Conf., IEEE, 1979.

    Google Scholar 

  19. Zames, G.: ‘Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms, and approximate inverses’, IEEE Trans. Auto. Control AC-26 (1981), 301–320.

    MathSciNet  Google Scholar 

  20. Helton, J.W.: ‘Operator theory and broadband matching’, in Proc. Allerton Conf., IEEE, 1979.

    Google Scholar 

  21. Tannenbaum, A.: ‘On the blending problem and parameter uncertainty in control theory’, Techn. Report Dept. Math. Weizmann Institute (1977).

    Google Scholar 

  22. Doyle, J.C. and Stein, G.: ‘Multivariable feedback design: concepts for a classical modern synthesis’, IEEE Trans. Auto. Control AC-26 (1981), 4–16.

    Google Scholar 

  23. Francis, B.A. and Doyle, J.C.: ‘Linear control theory with an H ∞ optimality criterion’, SIAM J. Control and Opt. 25 (1987), 815–844.

    MathSciNet  MATH  Google Scholar 

  24. Francis, B.A.: A course in H ∞ control theory, Lecture notes in control and information sci., 88, Springer, 1987.

    Google Scholar 

  25. Boardman, J. and Vogt, P.: Homotopy invariant algebraic structures on topological spaces, Springer, 1973.

    Google Scholar 

  26. Spanier, E.: Algebraic topology, McGraw-Hill, 1966.

    Google Scholar 

  27. Haag, R.: ‘On quantum field theories’, Danske Mat.-Fys. Medd. 29, no. 12 (1955), 17–112.

    MathSciNet  Google Scholar 

  28. Emch, G.: Algebraic methods in statistical mechanics and quantum field theory, Wiley, 1972.

    Google Scholar 

  29. Streit, L.: ‘Energy forms: Schroedinger theory, processes. New stochastic methods in physics’, Physics reports 77, no. 3 (1980), 363–375.

    MathSciNet  Google Scholar 

  30. Streater, R.F. and Wightman, A.S.: PCT, spin and statistics, and all that, Benjamin, 1964.

    Google Scholar 

  31. Haar, A.: ‘Die Minkowskische Geometrie and die Annäherung an stetige Funktionen’, Math, Ann. 78 (1918), 249–311.

    Google Scholar 

  32. Akhiezer, N.I.: Theory of approximation, F. Ungar, 1956 (translated from the Russian).

    Google Scholar 

  33. Cheney, E.W.: Introduction to approximation theory, McGraw-Hill, 1966, Chapt. 3.

    Google Scholar 

  34. Holland, A.S. and Sahney, B.N.: The general problem of approximation and spline functions, R.E. Krieger, 1979, Chapt. 2.

    Google Scholar 

  35. Lorentz, G.G. and Riemenschneider, S.D.: ‘Approximation and interpolation in the last 20 years’, in Birkhoff interpolation, Addison-Wesley, 1983, pp. xix-lv; in particular, xx-xxiii.

    Google Scholar 

  36. Timan, A.F.: Theory of approximation of functions of a real variable, Pergamon, 1963, Chapt. 2 (translated from the Russian).

    Google Scholar 

  37. Rice, J.R.: The approximation of functions, 1, Addison-Wesley, 1964.

    Google Scholar 

  38. Meinardus, G.: Approximation of functions: theory and numerical methods, Springer, 1967.

    Google Scholar 

  39. Bridges, D.S.: ‘Recent developments in constructive approximation theory’, in A.S. Troelstra and D. van Dalen (eds.): The L.E.J. Brouwer Centenary Symposium, North-Holland, 1982, pp. 41-50.

    Google Scholar 

  40. Haar, A.: ‘Der Massbegriff in der Theorie der kontinuierlichen Gruppen’, Ann. of Math. (2) 34 (1933), 147–169.

    MathSciNet  Google Scholar 

  41. Bourbaki, N.: Elements of mathematics. Integration, Addison-Wesley, 1975, Chapt 6; 7; 8 (translated from the French).

    Google Scholar 

  42. Weil, A.: l’Intégration dans les groupes topologiques et ses applications, Hermann, 1940.

    Google Scholar 

  43. Loomis, L.H.: An introduction to abstract harmonic analysis, v. Nostrand, 1953.

    Google Scholar 

  44. Helgason, S.: Differential geometry and symmetric spaces, Acad. Press, 1962.

    Google Scholar 

  45. Hewitt, E. and Ross, K.A.: Abstract harmonic analysis, 1–2, Springer, 1979.

    Google Scholar 

  46. Haar, A.: ‘Zur Theorie der orthogonalen Funktionensysteme’, Math. Ann. 69 (1910), 331–371.

    MathSciNet  MATH  Google Scholar 

  47. Alexits, G. [G. Aleksits]: Convergence problems of orthogonal series, Pergamon, 1961 (translated from the Russian).

    Google Scholar 

  48. Ul’yanov, P.L.: ‘On Haar series’, Mat. Sb. 63, no. 3 (1964), 356–391 (in Russian).

    MathSciNet  Google Scholar 

  49. Ul’yanov, P.L.: ‘Absolute and uniform convergence of Fourier series’, Math. USSR Sb. 1, no. 2 (1967), 169–197. (Mat. Sb. 72, no. 2 (1967), 193-225)

    MathSciNet  Google Scholar 

  50. Golubov, B.I.: ‘Series with respect to the Haar system’, J. Soviet Math. 1 (1971), 704–726. (Itogi. Nauk. Mat. Anal 1970 (1971), 109-143)

    Google Scholar 

  51. Kashin, B.S. and Saakyan, A.A.: Orthogonal series, Moscow, 1984 (in Russian).

    Google Scholar 

  52. Singer, I.M.: Bases in Banach spaces, 1–2, Springer, 1970–1981.

    Google Scholar 

  53. Undenstrauss, J. and Tzafriri, L.: Classical Banach spaces, 1–2, Springer, 1977–1979.

    Google Scholar 

  54. Hadamard, J.: ‘Résolution d’une question relative aux déterminants’, Bull. Sci. Math. (2) 17 (1893), 240–246.

    MATH  Google Scholar 

  55. Hall, M: Combinatorial theory, Blaisdell, Waltham (MA), 1967, Chapt. 14.

    Google Scholar 

  56. Peterson, W.W.: Error-correcting codes, M.I.T. & Wiley, 1961.

    Google Scholar 

  57. Butson, A.T.: ‘Generalized Hadamard matrices’, Proc. Amer. Math. Soc. 13 (1962), 894–898.

    MathSciNet  MATH  Google Scholar 

  58. Wallis, W.D., Street, A.P. and Wallis, J.S.: Combinatorics: room squares, sum-free sets, Hadamard matrices, Springer, 1972.

    Google Scholar 

  59. Hughes, D.R. and Piper, F.C.: Design theory, Cambridge Univ. Press, 1988.

    Google Scholar 

  60. MacWilliams, F.J. and Sloane, N.J.A.: The theory of error correcting codes, I–II, North-Holland, 1977.

    Google Scholar 

  61. Agaian, S.S.: Hadamard matrices and their applications, Lecture notes in math., 1168, Springer, 1985.

    Google Scholar 

  62. Beth, T., Jungnickel, D. and Lenz, H.: Design theory, Cambridge Univ. Press, 1986.

    Google Scholar 

  63. Hedayat, A. and Wallis, W.D.: ‘Hadamard matrices and their applications’, Ann. Stat. 6 (1978), 1184–1238.

    MathSciNet  MATH  Google Scholar 

  64. Hadamard, J.: ‘Essai sur l’étude des fonctions données par leurs développement de Taylor’, J. Math. Pures Appl. (4) 8 (1892), 101–186.

    MATH  Google Scholar 

  65. Bieberbach, L.: Analytische Fortsetzung, Springer, 1955.

    Google Scholar 

  66. Hadamard, J.: ‘Étude sur les propriétés des fonctions entières et en particulier d’une fonction considérée par Riemann’, J. Math. Pures Appl. (4) 9 (1893), 171–215.

    MATH  Google Scholar 

  67. Markushevich, A.I.: Theory of Junctions of a complex variable, 1, Chelsea, 1977 (translated from the Russian).

    Google Scholar 

  68. Levin, B.Ya.: Distributions of zeros of entire functions, Amer. Math. Soc., 1964 (translated from the Russian).

    Google Scholar 

  69. Boas, R.P.: Entire functions, Acad. Press, 1954.

    Google Scholar 

  70. Titchmarsh, E.C.: The theory of functions, Oxford Univ. Press, 1979.

    Google Scholar 

  71. Hadamard, J.: ‘Résolution d’une question relative aux déterminants’, Bull. Sci. Math. (2) 17 (1893), 240–246.

    MATH  Google Scholar 

  72. Hadamard, J.: ‘Sur la distribution des zéros de la fonction s(s) et ses conséquences arithmétiques’, Bull. Soc. Math. France 24 (1896), 199–220.

    MathSciNet  MATH  Google Scholar 

  73. Markushevich, A.I.: Theory of fonctions of a complex variable, 1, Chelsea, 1977 (translated from the Russian).

    Google Scholar 

  74. Privalov, I.I.: Subharmonic functions, Moscow-Leningrad, 1937 (in Russian).

    Google Scholar 

  75. Solomentsev, E.D.: ‘A three-sphere theorem for harmonic functions’, Dokl. Akad. Nauk ArmSSR 42, no. 5 (1966), 274–278 (in Russian).

    Google Scholar 

  76. Boas, R.P.: Entire functions, Acad. Press, 1964.

    Google Scholar 

  77. Titchmarsh, E.C.: The theory of functions, Oxford Univ. Press, 1979.

    Google Scholar 

  78. Hadamard, J.: ‘Théorème sur les series entières’, Acta Math. 22 (1899), 55–63.

    MathSciNet  Google Scholar 

  79. Hadamard, J.: ‘La série de Taylor et son prolongement analytique’, Scientia Phys.-Math., no. 12 (1901).

    Google Scholar 

  80. Bieberbach, L.: Analytische Fortsetzung, Springer, 1955.

    Google Scholar 

  81. Boas, R.P.: Entire functions, Acad. Press, 1954.

    Google Scholar 

  82. Titchmarsh, E.C.: The theory of functions, Oxford Univ. Press, 1979.

    Google Scholar 

  83. Pommerenke, E.: Univalent functions, Vandenhoeck & Ruprecht, 1975.

    Google Scholar 

  84. Hadamard, J.: ‘Memoire sur le problème d’analyse relatif a l’équilibre des plagues élastiques eucastrées’, Mém. prés, par divers savants à l’Acad. Sci. 33 (1907). Also: Oeuvres, Vol. II, C.N.R.S. (1968), pp. 515-631.

    Google Scholar 

  85. Schiffer, M. and Spencer, D.C.: Functionals of finite Kiemann surfaces, Princeton Univ. Press, 1954.

    Google Scholar 

  86. Warschawski, S.E.: ‘On Hadamard’s variation formula for Green’s function’, J. Math. Mech. 9 (1960), 497–511.

    MathSciNet  MATH  Google Scholar 

  87. Hadwiger, H.: ‘Ueber Treffanzahlen bei translationsgleichen Eikörpern’, Arch. Math. (Basel) 8 (1957), 212–213.

    MATH  Google Scholar 

  88. Boltyanskiĭ, V.G. and Soltan, P.S.: Combinatorial geometry of various classes of convex sets, Kishinev, 1978 (in Russian).

    Google Scholar 

  89. Lassak, M.: ‘Solution of Hadwiger’s covering problem for centrally symmetric convex bodies in E 3’, J. London Math. Soc. (2) 30 (1984), 501–511.

    MathSciNet  MATH  Google Scholar 

  90. Danzer, L., Grünbaum, B. and Klee, V.: ‘Helly’s theorem and its relatives’, in V. Klee (ed.): Convexity, Proc. Symp. Pure Math., Vol. 7, Amer. Math. Soc., 1963, pp. 101-180.

    Google Scholar 

  91. Hadwiger, H. and Debrunner, H.: ‘Kombinatorische Geometrie in der Ebene’, L’Enseign. Math. 2 (1959).

    Google Scholar 

  92. Gruber, P.M. and Lekkerkerker, C.G.: Geometry of numbers, North-Holland, 1987.

    Google Scholar 

  93. Haefliger, A.: ‘Feuilletages sur les variétés ouvertes’, Topology 9, no. 2 (1970), 183–194.

    MathSciNet  MATH  Google Scholar 

  94. Haefliger, A.: ‘Homotopy and integrability’, in N.H. Kuiper (ed.): Manifolds: Amsterdam 1970, Lecture notes in math., Vol. 197, Springer, 1971, pp. 133-163.

    Google Scholar 

  95. Lawson, H.: The quantitative theory of foliations, Amer. Math. Soc., 1977.

    Google Scholar 

  96. Fuks, D.B.: ‘Cohomology of infinite-dimensional Lie algebras and characteristic classes of foliations’, J. Soviet Math. 11 (1979), 922–980. (Itogi Nauk. i Tekhn. Sovrem. Probl. Mat. 10 (1978), 179-285)

    Google Scholar 

  97. Fuks, D.B.: ‘Foliations’, J. Soviet Math. 18 (1982), 255–291. (Itogi Nauk. i Tekhn. Algebra Topol. Geom. 18 (1981), 151-213)

    Google Scholar 

  98. Hahn, H.: ‘Ueber lineare Gleichungsysteme in linearen Räume’, J. Reine Angew. Math. 157 (1927), 214–229.

    MATH  Google Scholar 

  99. Banach, S.: ‘Sur les fonctionelles linéaires’, Studia Math. 1 (1929), 211–216.

    MATH  Google Scholar 

  100. Banach, S.: ‘Sur les fonctionelles linéaires II’, Studia Math. 1 (1929), 223–239.

    MATH  Google Scholar 

  101. Kolmogorov, A.N. and Fomin, S.V.: Elements of the theory of functions and functional analysis, Graylock, 1957–1961 (translated from the Russian).

    Google Scholar 

  102. Kantorovich, L.V. and Akilov, G.P.: Functional analysis, Pergamon, 1982 (translated from the Russian).

    Google Scholar 

  103. Dunford, N. and Schwartz, J.T.: Linear operators. General theory, 1, Interscience, 1958.

    Google Scholar 

  104. Köthe, G.: Topological vector spaces, Springer, 1969.

    Google Scholar 

  105. Dunford, N. and Schwartz, J.T.: Linear operators. General theory, 1, Interscience, 1958.

    Google Scholar 

  106. Halmos, P.R.: Measure theory, v. Nostrand, 1950.

    Google Scholar 

  107. Rudin, W.: Real and complex analysis, McGraw-Hill, 1966.

    Google Scholar 

  108. Royden, H.L.: Real analysis, Macmillan, 1968.

    Google Scholar 

  109. Chunikhin, S.A.: Subgroups of finite groups, Wolters-Noordhoff, 1969 (translated from the Russian).

    Google Scholar 

  110. Itogi Nauk. i Tekhn. Algebra. 1964 (1966), 7-46.

    Google Scholar 

  111. Huppert, B.: Endliche Gruppen, 1, Springer, 1979.

    Google Scholar 

  112. Gorenstein, D. (ed.): Reviews on finite groups, Amer. Math. Soc., 1974.

    Google Scholar 

  113. Halphen, G.H.: ‘Sur les courbes planes du sixième degré à neuf points double’, Bull. Soc. Math. France 10 (1882), 162–172.

    MathSciNet  MATH  Google Scholar 

  114. Bertini, E.: Ann. Mat. Pura Appl. 8 (1877), 224–286.

    Google Scholar 

  115. Dolgachev, I.V.: ‘On rational surfaces with a pencil of elliptic curves’, Izv. Akad. Nauk SSSR Ser. Mat. 30 (1966), 1073–1100 (in Russian).

    MathSciNet  MATH  Google Scholar 

  116. Hamilton, W.R.: Philos. Transact. Roy. Soc London Ser. A 1 (1835), 95–144.

    Google Scholar 

  117. Arnol’d, V.I.: Mathematical methods of classical mechanics, Springer, 1978 (translated from the Russian).

    Google Scholar 

  118. Bliss, G.A.: Lectures on the calculus of variations, Chicago Univ. Press, 1947.

    Google Scholar 

  119. Pontryagin, et al., L.S.: The mathematical theory of optimal processes, Wiley, 1962 (translated from the Russian).

    Google Scholar 

  120. Goldstein, H.: Classical mechanics, Addison-Wesley, 1950.

    Google Scholar 

  121. Crouch, P.E. and Schaft, A.J. van der: Variational Hamiltonian control systems, Lecture notes in control and inform., 101, Springer, 1987.

    Google Scholar 

  122. Arnol’d, V.I.: Mathematical methods of classical mechanics, Springer, 1978 (translated from the Russian).

    Google Scholar 

  123. Hall, M.: The theory of groups, Macmillan, 1959.

    Google Scholar 

  124. Huppert, B.: Endliche Gruppen, 1, Springer, 1967.

    Google Scholar 

  125. Variational principles of mechanics, Moscow, 1959 (in Russian).

    Google Scholar 

  126. Pars, L.A.: A treatise on analytical dynamics, Heinemann, 1965.

    Google Scholar 

  127. Arnol’d, V.I.: Mathematical methods of classical mechanics, Springer, 1978 (translated from the Russian).

    Google Scholar 

  128. Akhiezer, N.I.: The calculus of variations, Blaisdell, 1962 (translated from the Russian).

    Google Scholar 

  129. Goldstein, H.: Classical mechanics, Addison-Wesley, 1950.

    Google Scholar 

  130. Lions, P.L.: Generalized solutions of Hamilton—Jacobi equations, Pitman, 1982.

    Google Scholar 

  131. Fleming, W. and Rishel, R.: Deterministic and stochastic optimal control, Springer, 1975.

    Google Scholar 

  132. Lions, P.L.: ‘On the Hamilton—Jacobi—Bellman equations’, Acta. Appl. Math. 1 (1983), 17–41.

    MathSciNet  MATH  Google Scholar 

  133. Benton, S.H., Jr.: The Hamilton—Jacobi equation: a global approach, Acad. Press., 1977.

    Google Scholar 

  134. Hamilton, W.R.: Lectures on quaternions, Dublin, 1853.

    Google Scholar 

  135. Rutherford, D.E.: Vector mechanics, Oliver & Boyd, 1949.

    Google Scholar 

  136. Apostol, T.M.: Calculus, 1–2, Blaisdell, 1964.

    Google Scholar 

  137. Holman, H. and Rummler, H.: Alternierende Differentialformen, Bl Wissenschaftsverlag, 1972.

    Google Scholar 

  138. Hamilton, W.: Report of the 4-th meeting of the British Association for the Advancement of Science, London, 1835, pp. 513-518.

    Google Scholar 

  139. Ostrogradski, M.: Mem. Acad. Sci. St. Petersbourg 8, no. 3 (1850), 33-48.

    Google Scholar 

  140. Arnol’d, V.l.: Mathematical methods of classical mechanics, Springer, 1978 (translated from the Russian).

    Google Scholar 

  141. Pars, L.A.: A treatise on analytical dynamics, Heinemann, 1965.

    Google Scholar 

  142. Arnol’d, V.I.: Mathematical methods of classical mechanics, Springer, 1978 (translated from the Russian).

    Google Scholar 

  143. Levi-Civita, T. and Amaldi, U.: Lezioni di meccanica razionale, 2, Zanichelli, 1951.

    Google Scholar 

  144. Whittaker, E.T.: Analytical dynamics of particles and rigid bodies, Dover, reprint, 1944.

    Google Scholar 

  145. Moser, J.: ‘Various aspects of integrable Hamiltonian systems’, in J. Guckenheimer, J. Moser and Sh.E. Newhouse (eds.): Dynamical Systems, Birkhäuser, 1980, pp. 233-289.

    Google Scholar 

  146. Arnol’d, V.I., et al.: Encycl. of Math. Sri., 3; 4; 7, Springer, 1988-(translated from the Russian).

    Google Scholar 

  147. Fomento, A.T.: Integrability and nonintegrability in geometry and mechanics, Kluwer, 1988 (translated from the Russian).

    Google Scholar 

  148. Faddeev, L.D. and Takhtajan, L.A.: Hamiltonian methods in the theory of solitons, Springer, 1987 (translated from the Russian).

    Google Scholar 

  149. Drazin, P.G.: Solitons, Cambridge Univ. Press, 1983.

    Google Scholar 

  150. Lyapunov, A.M.: Problème général de la stabilité du mouvement, Princeton Univ. Press, 1947 (translated from the Russian). Reprint: Krauss, 1950.

    Google Scholar 

  151. Kreĭn, M.G.: ‘Foundations of the theory of λ-zones of stability of a canonical system of linear differential equations with periodic coefficients’, Transl. Amer. Math Soc. (2) 120 (1983), 1–70. (In memoriam: A.A. Andronov (1955), 413-498)

    Google Scholar 

  152. Yakubovich, V.A. and Starzhinskiĭ, V.M.: Linear differential equations with periodic coefficients, Wiley, 1975 (translated from the Russian).

    Google Scholar 

  153. Gel’fand, I.M. and Lidskiĭ, V.B.: ‘On the structure of stability regions of linear canonical systems of differential equations with periodic coefficients’, Uspekhi Mat. Nauk 10, no. 1 (1955), 3–40 (in Russian).

    Google Scholar 

  154. Sternberg, R.L.: ‘Variational methods and non-oscillation theorems for systems of differential equations’, Duke Math. J. 19 (1952), 311–322.

    MathSciNet  MATH  Google Scholar 

  155. Yakubovich, V.A.: ‘Oscillatory properties of solutions of canonical equations’, Mat. Sb. 56 (96), no. 1 (1962), 3–42 (in Russian).

    MathSciNet  Google Scholar 

  156. Kreĭn, M.G.: ‘Hamiltonian systems of linear differential equations with periodic coefficients’, Transl. Amer. Math. Soc. (2) 120 (1983), 139–168. (Proc. Intern. Symp. Non-Linear Oscillations 1 (1963), 277-305)

    Google Scholar 

  157. Lidskiĭ, V.B.: ‘Oscillation theorems for canonical systems of differential equations’, Dokl. Akad. Nauk SSSR 102, no. 5 (1955), 877–880 (in Russian).

    MathSciNet  Google Scholar 

  158. Derguzov, V.M.: ‘On stability of the solutions of the Hamilton equation with unbounded periodic operator coefficients’, Mat. Sb. 63 (105), no. 4 (1964), 591–619 (in Russian).

    MathSciNet  Google Scholar 

  159. Moser, J.: ‘New aspects in the theory of stability of Hamiltonian systems’, Comm. Pure Appl. Math. 11 (1958), 81–114.

    MathSciNet  MATH  Google Scholar 

  160. Coppel, W.A. and Howe, A.: ‘On the stability of linear canonical systems with periodic coefficients’, J. Austral. Math. Soc. 5 (1965), 169–195.

    MathSciNet  Google Scholar 

  161. Mitropol’skiĭ, Yu.A.: An averaging method in non-linear mechanics, Kiev, 1971 (in Russian).

    Google Scholar 

  162. Erugin, N.P.: Linear systems of ordinary differential equations with periodic and quasi-periodic coefficients, Acad. Press, 1966 (translated from the Russian).

    Google Scholar 

  163. Lidskiĭ, V.B. and Frolov, P.A.: ‘The structure of the domain of stability of a self-adjoint system of differential equations with periodic coefficients’, Mat. Sb. 71 (113), no. 1 (1966), 48–64 (in Russian).

    MathSciNet  Google Scholar 

  164. Daletskiĭ, Yu.L. and Kreĭn, M.G.: Stability of solutions of differential equations in Banach space, Amer. Math. Soc., 1974 (translated from the Russian).

    Google Scholar 

  165. Fomin, V.N.: Mathematical theory of parameter resonance in linear distributed systems, Leningrad, 1972 (in Russian).

    Google Scholar 

  166. Hammerstein, A.: ‘Nichtlineare Integralgleichungen nebst Anwendungen’, Acta Math. 54 (1930), 117–176.

    MathSciNet  MATH  Google Scholar 

  167. Tricomi, F.G.: Integral equations, Dover, reprint, 1985.

    Google Scholar 

  168. Vaĭnberg, M.M.: Variational methods far the study of nonlinear operators, Holden-Day, 1964 (translated from the Russian).

    Google Scholar 

  169. Krasnosel’skiĭ, M.A.: Topological methods in the theory of nonlinear integral equations, Pergamon, 1964 (translated from the Russian).

    Google Scholar 

  170. Smirnov, N.S.: Introduction to the theory of integral equations, Moscow-Leningrad, 1936 (in Russian).

    Google Scholar 

  171. Smale, S.: ‘Generalised Poincaré conjecture in dimensions >4’, Ann. of Math (2) 74 (1961), 391–466.

    MathSciNet  MATH  Google Scholar 

  172. Smale, S.: ‘Structure of manifolds’, Amer. J. Math. 84 (1962), 387–399.

    MathSciNet  MATH  Google Scholar 

  173. Smale, S.: ‘A survey of some recent developments in differential topology’, Bull. Amer. Math. Soc. 69 (1963), 131–145.

    MathSciNet  Google Scholar 

  174. Kirby, R.C. and Siebenmann, L.C.: Foundational essays on topological manifolds, smoothings, and triangulations, Princeton Univ. Press, 1977.

    Google Scholar 

  175. Rourke, K. and Sanderson, B.: Introduction to piecewise linear topology, Springer, 1972.

    Google Scholar 

  176. Rokhlin, V.A. and Fuks, D.B.: Beginner’s course in topology. Geometric chapters, Springer, 1984 (translated from the Russian).

    Google Scholar 

  177. Milnor, J.: Morse theory, Princeton Univ. Press, 1963.

    Google Scholar 

  178. Milnor, J.: Lectures on the h-cobordism theorem, Princeton Univ. Press, 1965.

    Google Scholar 

  179. Jahnke, E., Emde, F. and Lösch, F.: Tafeln höheren Funktionen, Teubner, 1966.

    Google Scholar 

  180. Riesz, F.: ‘Ueber die Randwerte einer analytischen Funktion’, Math. Z. 18 (1923), 87–95.

    MathSciNet  MATH  Google Scholar 

  181. Priwalow, I.I. [I.I. Privalov]: Randeigenschaften analytischer Funktimen, Deutsch. Verlag Wissenschaft., 1956 (translated from the Russian).

    Google Scholar 

  182. Stein, E. and Weiss, G.: ‘On the theory of harmonic functions of several variables’, Acta Math. 103 (1960), 25–62.

    MathSciNet  MATH  Google Scholar 

  183. Hoffman, K.: Banach spaces of analytic functions, Prentice-Hall, 1962.

    Google Scholar 

  184. Duren, P.: Theory of H p-spaces, Acad. Press, 1970.

    Google Scholar 

  185. Rudin, W.: Function theory in polydiscs, Benjamin, 1969.

    Google Scholar 

  186. Coifman, R.R. and Weiss, G.: ‘Extensions of Hardy spaces and their use in analysis’, Bull. Amer. Math. Soc. 83, no. 4 (1977), 569–645.

    MathSciNet  MATH  Google Scholar 

  187. Petersen, K.E.: Brownian motion, Hardy spaces, and bounded mean oscillation, Cambridge Univ. Press, 1977.

    Google Scholar 

  188. Koosis, P.: Introduction to H p-spaces. With an appendix on Wolff’s proof of the corona theorem, Cambridge Univ. Press, 1980.

    Google Scholar 

  189. Rudin, W.: Function theory in the unit ball of C n, Springer, 1980.

    Google Scholar 

  190. Folland, G.B. and Stein, E.M.: Hardy spaces on homogeneous groups, Princeton Univ. Press, 1982.

    Google Scholar 

  191. Gamelin, T.: Uniform algebras, Prentice-Hall, 1969.

    Google Scholar 

  192. Garnett, J.: Bounded analytic functions, Acad. Press, 1981.

    Google Scholar 

  193. Fefferman, C. and Stein, E.M.: ‘H p spaces of several variables’, Acta Math. 129 (1972), 137–193.

    MathSciNet  MATH  Google Scholar 

  194. Hardy, G.H.: ‘Some theorems connected with Abel’s theorem on the continuity of power series’, Proc. London. Math. Soc. (2) 4 (1907), 247–265.

    Google Scholar 

  195. Rudin, W.: Principles of mathematical analysis, McGraw-Hill, 1976.

    Google Scholar 

  196. Hardy, G.H., Littlewood, J.E. and Pólya, G.: Inequalities, Cambridge Univ. Press, 1934.

    Google Scholar 

  197. Nikol’skiĭ, S.M.: Approximation of functions of several variables and imbedding theorems, Springer, 1975 (translated from the Russian).

    Google Scholar 

  198. Muckenhoupt, B.: ‘Hardy’s inequality with weights’, Studia Math. 44 (1972), 31–38.

    MathSciNet  MATH  Google Scholar 

  199. Hardy, G.H. and Littlewood, J.E: ‘Some new convergece criteria for Fourier series’, J. London. Math. Soc. 7 (1932), 252–256.

    MathSciNet  Google Scholar 

  200. Bary, N.K. [N.K. Bari]: A treatise on trigonometric series, Pergamon, 1964 (translated from the Russian).

    Google Scholar 

  201. Linnik, Yu.V.: The dispersion method in binary additive problems, Amer. Math. Soc., 1963 (translated from the Russian).

    Google Scholar 

  202. Bredkhin, B.M. and Linnik, Yu.V.: ‘Asymptotic behaviour and ergodic properties of solutions of the generalized Hardy—Littlewood equation’, Mat. Sb. 71, no. 2 (1966), 145–161 (in Russian).

    MathSciNet  Google Scholar 

  203. Bredkhin, B.M.: ‘The dispersion method and definite binary additive problems’, Russian Math. Surveys 20, no. 2 (1965), 85–125. (Uspekhi Mat. Nauk 20, no. 2 (1965), 89-130)

    Google Scholar 

  204. Hardy, G.H. and Littlewood, J.E.: ‘Tauberian theorems concerning power series and Dirichlet’s series whose coefficients are positive’, Proc. London. Math. Soc (2) 13 (1914), 174–191.

    MathSciNet  MATH  Google Scholar 

  205. Titchmarsh, E: The theory of functions, Oxford Univ. Press, 1979.

    Google Scholar 

  206. Hardy, G.H. and Littlewood, J.E.: ‘A maximal theorem with function-theoretic applications’, Acta. Math. 54 (1930), 81–116.

    MathSciNet  MATH  Google Scholar 

  207. Zygmund, A.: Trigonometric series, 1, Cambridge Univ. Press, 1988.

    Google Scholar 

  208. Stein, E.M. and Weiss, G.: Fourier analysis on Euclidean spaces, Princeton Univ. Press, 1971.

    Google Scholar 

  209. Hardy, G.H.: ‘The mean value of the modulus of an analytic function’, Proc. London. Math. Soc. (2) 14 (1915), 269–277.

    MATH  Google Scholar 

  210. Privalov, I.I.: Subharmonic functions, Moscow-Leningrad, 1937 (in Russian).

    Google Scholar 

  211. Rado, T.: Subharmonic functions, Springer, 1937.

    Google Scholar 

  212. Duren, P.: Theory of H p spaces, Acad. Press, 1970.

    Google Scholar 

  213. Doob, J.L.: Classical potential theory and its probabilistic counterpart, Springer, 1984.

    Google Scholar 

  214. Hardy, G.H.: ‘Some formulae in the theory of Bessel functions’, Proc. London. Math. Soc. (2) 23 (1925), 61–63.

    Google Scholar 

  215. Brychkov, Yu.A. and Prudnikov, A.P.: Integral transforms of generalized functions, Gordon & Breach, 1989 (translated from the Russian).

    Google Scholar 

  216. Hardy, G.H.: ‘On double Fourier series and especially those which represent the double zeta-function with real and incommensurable parameters’, Quarterly J. Math. 37 (1905), 53–79.

    MATH  Google Scholar 

  217. Hahn, H.: Theorie der reellen Funktionen, 1, Springer, 1921.

    Google Scholar 

  218. Ash, J.M. (ed.): Studies in harmonic analysis, Math. Assoc. Amer., 1976.

    Google Scholar 

  219. Katznelson, Y.: An introduction to harmonic analysis, Dover, reprint, 1976.

    Google Scholar 

  220. Peter, F. and Weyl, H.: ‘Die Vollständigkeit der primitiven Darstellungen einer geschlossener kontinuierlichen Gruppe’, Math. Ann. 97 (1927), 737–755.

    MathSciNet  MATH  Google Scholar 

  221. Pontryagin, L.S.: ‘The theory of commutative topological groups’, Ann. of Math. (2) 35, no. 2 (1934), 361–388 (in Russian).

    MathSciNet  MATH  Google Scholar 

  222. Kampen, E.R. van: Proc. Nat. Acad. Sci. USA 20 (1934), 434–436.

    Google Scholar 

  223. Weil, A.: l’Intégration dans les groupes topologiques et ses applications, Hermann, 1940.

    Google Scholar 

  224. Gel’fand, I.M. and Raĭkov, D.A.: ‘Nondegenerate unitary representations of locally (bi)compact groups’, Mat. Sb. 13 (55) (1943), 301–316 (in Russian). English abstract.

    Google Scholar 

  225. Raĭkov, D.A.: ‘Harmonic analysis on commutative groups with the Haar measure and character theory’, Trudy Mat. Inst. Steklov. 14 (1945), 1–86 (in Russian). English abstract.

    Google Scholar 

  226. Gelfand, I.M. [I.M. Gel’fand], Raikov, D.A. [D.A. Raĭkov] and Schilow, G.E. [G.E. Shilov]: Kommutative Normierte Ringe, Deutsch. Verlag Wissenschaft., 1964 (translated from the Russian).

    Google Scholar 

  227. Naĭmark, M.A.: Normed rings, Reidel, 1984 (translated from the Russian).

    Google Scholar 

  228. Pontryagin, L.S.: Topological groups, Princeton Univ. Press, 1958 (translated from the Russian).

    Google Scholar 

  229. Bourbaki, N.: Elements of mathematics. Spectral theories, Addison-Wesley, 1977 (translated from the French).

    Google Scholar 

  230. Dixmier, J.: C* algebras, North-Holland, 1977 (translated from the French).

    Google Scholar 

  231. Helson, H., et al.: ‘The functions which operate on Fourier transforms’, Acta Math. 102 (1959), 135–157.

    MathSciNet  MATH  Google Scholar 

  232. Hewitt, E. and Ross, K.A.: Abstract harmonic analysis, 1–2, Springer, 1963–1970.

    Google Scholar 

  233. Loomis, L.H.: An introduction to abstract harmonic analysis, v. Nostrand, 1953.

    Google Scholar 

  234. Malliavin, P.: ‘Impossibilité de la synthèse spectrale sur les groupes abéliens non compacts’, Publ. Math IHES 2 (1959), 61–68.

    MATH  Google Scholar 

  235. Kreĭn, M.G.: ‘Sur une généralisation du théorème de Plancherel au cas des intégrales de Fourier sur les groupes topologiques commutatifs’, Dokl. Akad. Nauk SSSR 30 (1941), 484–488.

    Google Scholar 

  236. Drury, S.W.: ‘Sur les ensembles de Sidon’, C.R. Acad. Sci. Paris A271 (1970), 162–163.

    MathSciNet  Google Scholar 

  237. Varopoulos, N.Th.: ‘Sur la réunion de deux ensembles de Helson’, C.R. Acad. Sci. Paris A271 (1970), 251–253.

    MathSciNet  Google Scholar 

  238. Rudin, W.: Fourier analysis on groups, Wiley, 1962.

    Google Scholar 

  239. Reiter, H.: Classical harmonic analysis and locally compact groups, Clarendon Press, 1968.

    Google Scholar 

  240. Lindahl, L.-Å. and Poulsen, F.: Thin sets in harmonic analysis, M. Dekker, 1971.

    Google Scholar 

  241. Graham, C.C. and McGehee, O.C.: Essays in commutative harmonic analysis, Springer, 1979.

    Google Scholar 

  242. López, J. and Ross, K.: Sidon sets, M. Dekker, 1975.

    Google Scholar 

  243. Krylov, N.M. and Bogolyubov, N.N.: Introduction to non-linear mechanics, Princeton Univ. Press, 1947 (translated from the Russian).

    Google Scholar 

  244. Bogolyubov, N.N. and Mitropol’skiĭ, Yu.A.: Asymptotic methods in the theory of non-linear oscillations, Hindushtan Publ. Comp., Delhi, 1961 (translated from the Russian).

    Google Scholar 

  245. Popov, E.P. and Pal’tov, I.P.: Approximate methods for studying non-linear automatic systems, Translation Services, Ohio, 1963 (translated from the Russian).

    Google Scholar 

  246. Fock, V.A. [V.A. Fok]: The theory of space, time and gravitation, Macmillan, 1954 (translated from the Russian).

    Google Scholar 

  247. Besse, A.L.: Einstein manifolds, Springer, 1987.

    Google Scholar 

  248. ‘Elie Cartan et les mathématiques d’auyourd’hui’, Astérisque (1985).

    Google Scholar 

  249. Hodge, W.V.D.: The theory and applications of harmonic integrals, Cambridge Univ. Press, 1952.

    Google Scholar 

  250. Rham, G. de: Differentiable manifolds, Springer, 1984 (translated from the French).

    Google Scholar 

  251. Schwartz, L.: Equaciones diferenciales parciales elipticas, Univ. Nac. Colombia, 1973.

    Google Scholar 

  252. Schwartz, L.: Variedades analiticas complejas, Univ. Nac. Colombia, 1956.

    Google Scholar 

  253. Wells, jr., R.O.: Differential analysis on complex manifolds, Springer, 1980.

    Google Scholar 

  254. Chern, S.S.: Complex manifolds without potential theory, Springer, 1979.

    Google Scholar 

  255. Goldberg, S.I.: Curvature and homology, Acad. Press, 1962.

    Google Scholar 

  256. Yano, K. and Bochner, S.: Curvature and Betti numbers, Princeton Univ. Press, 1953.

    Google Scholar 

  257. Matsushima, Y. and Murakami, S.: ‘On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds’, Ann. of Math. 78 (1963), 365–416.

    MathSciNet  MATH  Google Scholar 

  258. Kohn, J.J.: ‘Harmonic integrals on strongly pseudoconvex manifolds I’, Ann. of Math. 78 (1963), 112–148.

    MathSciNet  MATH  Google Scholar 

  259. Kohn, J.J.: ‘Harmonic integrals on strongly pseudoconvex manifolds II’, Ann. of Math. 79 (1964), 450–472.

    MathSciNet  MATH  Google Scholar 

  260. Timan, A.F. and Trofimov, V.N.: Introduction to the theory of harmonic functions, Moscow, 1968 (in Russian).

    Google Scholar 

  261. Günter, N.M. [N.M. Gyunter]: Potential theory and its applications to basic problems of mathematical physics, F. Ungar, 1967 (translated from the Russian).

    Google Scholar 

  262. Sretenskiĭ, L.N.: Theory of the Newton potential, Moscow-Leningrad, 1946 (in Russian).

    Google Scholar 

  263. Brélot, M.: Eléments de la théorie classique du potentiel, Sorbonne Univ. Centre Doc. Univ., Paris, 1959.

    Google Scholar 

  264. Kellogg, O.D.: Foundations of potential theory, Springer, 1967. Re-issue: Springer, 1967.

    Google Scholar 

  265. Vladimirov, V.S.: Equations of mathematical physics, Mir, 1984 (translated from the Russian).

    Google Scholar 

  266. Lavrent’ev, M.A. and Shabat, B.V.: Methoden der komplexen Funktionentheorie, Deutsch. Verlag Wissenschaft., 1967 (translated from the Russian).

    Google Scholar 

  267. Markushevich, A.I.: Theory of functions of a complex variable, 2, Chelsea, 1977 (translated from the Russian).

    Google Scholar 

  268. Lavrentiev, M.M. [M.M. Lavrent’ev]: Some improperly posed problems of mathematical physics, Springer, 1967 (translated from the Russian).

    Google Scholar 

  269. Mergelyan, S.N.: ‘Harmonic approximation and approximate solution of Cauchy’s problem for the Laplace equation’, Uspekhi Mat. Nauk 11, no. 5 (1956), 3-26 (in Russian).

    Google Scholar 

  270. Priwalow, I.I. [I.I. Privalov]: Randeigenschaften analytischer Funktionen, Deutsch. Verlag Wissenschaft., 1956 (translated from the Russian).

    Google Scholar 

  271. Solomentsev, E.D.: ‘Harmonic and subharmonic functions and their generalizations’, Itogi Nauk. Ser. Mat., Mat. Anal., Teor. Veroyatnost., Regulirovanie, 1962 (1964), 83-100 (in Russian).

    Google Scholar 

  272. Fuglede, B.: Finely harmonic functions, Springer, 1972.

    Google Scholar 

  273. Hayman, W.K. and Kennedy, P.B.: Subharmonic functions, 1, Acad. Press, 1976.

    Google Scholar 

  274. Helms, L.L.: Introduction to potential theory, Wiley (Interscience), 1969.

    Google Scholar 

  275. Frostman, O.: ‘Potentiel d’équilibre et capacité des ensembles avec quelques applications à la théorie des fonctions’, Mett. Lunds Univ. Mat. Sem. 3 (1935), 1–118.

    Google Scholar 

  276. Brélot, M.: Eléments de la théorie classique du potentiel, Sorbonne Univ. Centre Doc. Univ., Paris, 1959.

    Google Scholar 

  277. Constantinescu, C. and Cornea, A.: Potential theory on harmonic spaces, Springer, 1972.

    Google Scholar 

  278. Carleman, T.: ‘Sur les fonctions inverses des fonctions entières d’ordre fini’, Ark. Mat. 15, no. 10 (1921), 1–7.

    Google Scholar 

  279. Nevanlinna, F. and Nevanlinna, R.: ‘Ueber die Eigenschaften einer analytischen Funktion in der Umgebung einer singulären Stelle oder Linie’, Acta Soc. Sci. Fennica 50, no. 5 (1922), 1–46.

    MathSciNet  Google Scholar 

  280. Vallée-Poussin, Ch.J. de la: Ann. Inst. H. Poincaré 2 (1932), 169–232.

    Google Scholar 

  281. Nevanunna, R.: Analytic functions, Springer, 1970 (translated from the German).

    Google Scholar 

  282. Goluzin, G.M.: Geometric theory of functions of a complex variable, Amer. Math. Soc., 1969 (translated from the Russian).

    Google Scholar 

  283. Brélot, M.: Eléments de la théorie classique du potentiel, Sorbonne Univ. Centre Doc. Univ., Paris, 1959.

    Google Scholar 

  284. Haliste, K.: ‘Estimates of harmonic measure’, Art Mat. 6, no. 1 (1965), 1–31.

    MathSciNet  MATH  Google Scholar 

  285. Constantinescu, C. and Cornea, A.: Potential theory on harmonic spaces, Springer, 1972.

    Google Scholar 

  286. Garnett, J.B.: Applications of harmonic measure, Wiley (Interscience), 1986.

    Google Scholar 

  287. Makarov, N.: ‘On the distortion of boundary sets under conformal mappings’, Proc. London Math. Soc. 51 (1985), 369–384.

    MathSciNet  MATH  Google Scholar 

  288. Nevanlinna, F. and Nevanlinna, R.: ‘Ueber die Eigenschaften einer analytischen Funktion in der Umgebung einer singulären Stelle oder Linie’, Acta Soc. Sci. Fennica 50, no. 5 (1922), 1–46.

    MathSciNet  Google Scholar 

  289. Nevanlinna, R.: Analytic functions, Springer, 1970 (translated from the German).

    Google Scholar 

  290. Sobolev, S.L.: Partial differential equations of mathematical physics, Pergamon, 1964 (translated from the Russian).

    Google Scholar 

  291. Tichonoff, A.N. [A.N. Tikhonov] and Samarskiĭ, A.A.: Differentialgleichungen der mathematischen Physik, Deutsch. Verlag Wissenschaft., 1959 (translated from the Russian).

    Google Scholar 

  292. Brélot, M.: Eléments de la théorie classique du potentiel, Centre Doc. Sorbonne Univ. Paris, 1959.

    Google Scholar 

  293. Berger, M.: Geometry, 1, Springer, 1987, p. 270 (translated from the French).

    Google Scholar 

  294. Coxeter, H.S.M.: Projective geometry, Blaisdell, 1964.

    Google Scholar 

  295. Coxeter, H.S.M.: The real projective plane, McGraw-Hill, 1949.

    Google Scholar 

  296. Hardy, G.H. and Wright, E.M.: An introduction to the theory of numbers, Oxford Univ. Press, 1979.

    Google Scholar 

  297. Brélot, M.: Lectures on potential theory, Tata Inst. Fundam. Res., 1960.

    Google Scholar 

  298. Bauer, H.: Harmonische Räume und ihre Potentialtheorie, Springer, 1966.

    Google Scholar 

  299. Constantinescu, C. and Cornea, A.: Potential theory on harmonic spaces, Springer, 1972.

    Google Scholar 

  300. Brelot, M: On topologies and boundaries in potential theory, Springer, 1971.

    Google Scholar 

  301. Bauer, H.: ‘Harmonische Räume’, in Jahrbuch Überblicke Mathematik, Bl Wissenschaftsverlag, 1981, pp. 9-35.

    Google Scholar 

  302. Brelot, M. (ed.): Potential theory. C.I.M.E. Stresa, 1969, Cremonese, 1970.

    Google Scholar 

  303. Gorelik, G.S.: Oscillations and waves, Moscow-Leningrad, 1950 (in Russian).

    Google Scholar 

  304. Rayleigh, J.W.S.: The theory of sound, 1, Dover, reprint, 1945.

    Google Scholar 

  305. Weyl, H.: ‘Harmonics on homogeneous manifolds’, Ann. of Math. 35 (1934), 486–499.

    MathSciNet  Google Scholar 

  306. Hobson, E.W.: The theory of spherical and ellipsoidal harmonics, Chelsea, reprint, 1955.

    Google Scholar 

  307. Loève, M.: Probability theory, 2, Springer, 1978.

    Google Scholar 

  308. Harnack, A.: Die Grundlagen der Theorie des logarithmischen Potentielles und der eindeutigen Potentialfunktion in der Ebene, Leipzig, 1887.

    Google Scholar 

  309. Courant, R. and Hilbert, D.: Methods of mathematical physics. Partial differential equations, 2, Interscience, 1965 (translated from the German).

    Google Scholar 

  310. Serrin, J.: ‘On the Harnack inequality for linear elliptic equations’, J. d’Anal. Math. 4, no. 2 (1955–1956), 292–308.

    MathSciNet  MATH  Google Scholar 

  311. Moser, J.: ‘On Harnack’s theorem for elliptic differential equations’, Comm. Pure Appl. Math. 14 (1961), 577–591.

    MathSciNet  MATH  Google Scholar 

  312. Moser, J.: ‘On Harnack’s theorem for parabolic differential equations’, Comm. Pure Appl. Math. 17 (1964), 101–134.

    MathSciNet  MATH  Google Scholar 

  313. Friedman, A.: Partial differential equations of parabolic type, Prentice-Hall, 1964.

    Google Scholar 

  314. Landis, E.M.: Second-order equations of elliptic and parabolic type, Moscow, 1971 (in Russian).

    Google Scholar 

  315. Boboc, N. and Mustatä, p.: Espaces harmoniques associés aux opérateurs différentiels linéaires du second order de type elliptique, Springer, 1968.

    Google Scholar 

  316. Helms, L.L.: Introduction to potential theory, Wiley (Interscience), 1969.

    Google Scholar 

  317. Harnack, A.: ‘Anwendung der Fourier’schen Reihe auf die Theorie der Funktionen einer komplexen Veränderlichen’, Math. Ann. 21 (1883), 305–326.

    MathSciNet  Google Scholar 

  318. Pesin, I.N.: Classical and modern integration theories, Acad. Press, 1970 (translated from the Russian).

    Google Scholar 

  319. Hobson, E.W.: The theory of functions of a real variable and the theory of Fourier’s series, 1, Dover, reprint, 1957.

    Google Scholar 

  320. Petrowski, I.G. [I.G. Petrovskiĭ]: Vorlesungen über partielle Differentialgleichungen, Teubner, 1965 (translated from the Russian).

    Google Scholar 

  321. Friedman, A.: Partial differential equations of parabolic type, Prentice-Hall, 1964.

    Google Scholar 

  322. Bony, J.-M.: ‘Opérateurs elliptiques dégénérés associés aux axiomatiques de la théorie du potentiel’, in Potential Theory, CIME, Stresa 1969, Cremonese, 1970, pp. 69-119.

    Google Scholar 

  323. Brélot, M.: Éléments de la théorie classique du potentiel, Sorbonne Univ. Centre Doc. Univ., 1959.

    Google Scholar 

  324. Constantinescu, C. and Cornea, A.: Potential theory on harmonic spaces, Springer, 1972.

    Google Scholar 

  325. Loeb, P. and Walsh, B.: ‘The equivalence of Harnack’s principle and Harnack’s inequality in the axiomatic system of Brélot’, Ann. Inst. Fourier 15, no. 2 (1965), 597–600.ai][1]_Vladimirov, V.S.: Methods of the theory of functions of several complex variables, M.I.T., 1966 (translated from the Russian).

    MathSciNet  MATH  Google Scholar 

  326. Bochner, S. and Martin, W.T.: Several complex variables, Princeton Univ. Press, 1948.

    Google Scholar 

  327. Behnke, H. and Thullen, P.: Theorie der Funktionen meherer komplexer Veränderlichen, Springer, 1970.

    Google Scholar 

  328. Vladdorov, V.S.: Methods of the theory of functions of several complex variables, M.I.T., 1966 (translated from the Russian).

    Google Scholar 

  329. Behnke, H. and Thullen, P.: Theorie der Funktionen mehrerer komplexer Veränderlichen, Springer, 1970.

    Google Scholar 

  330. Bochner, S. and Martin, W.T.: Several complex variables, Princeton Univ. Press, 1948.

    Google Scholar 

  331. Hartogs, F.: ‘Zur Theorie der analytischen Funktionen mehrerer unabhängiger Veränderlichen, insbesondere über die Darstellung derselber durch Reihen welche nach Potentzen einer Veränderlichen fortschreiten’, Math. Ann. 62 (1906), 1–88.

    MathSciNet  MATH  Google Scholar 

  332. Bochner, S. and Martin, W.T.: Several complex variables, Princeton Univ. Press, 1948.

    Google Scholar 

  333. Shabat, B.V.: Introduction to complex analysis, 1–2, Moscow, 1976 (in Russian).

    Google Scholar 

  334. Hormander, L.: An introduction to complex analysis in several variables, North-Holland, 1973.

    Google Scholar 

  335. Krantz, S.G.: Function theory of several complex variables, Wiley (Interscience), 1982.

    Google Scholar 

  336. Hasse, H.: ‘Ueber p-adische Schiefkörper und ihre Bedeutung für die Arithmetik hyperkomplexen Zahlsysteme’, Math. Ann. 104 (1931), 495–534.

    MathSciNet  Google Scholar 

  337. Hasse, H.: ‘Die Struktur der R. Brauerschen Algebren-klassengruppe über einem algebraischen Zahlkörper. Inbesondere Begründung der Theorie des Normenrestsymbols und Herleitung des Reziprozitätsgesetzes mit nichtkommutativen Hilfsmitteln’, Math. Ann. 107 (1933), 731–760.

    MathSciNet  Google Scholar 

  338. Cassels, J.W.S. and Fröhlich, A. (eds.): Algebraic number theory, Acad. Press, 1986.

    Google Scholar 

  339. Weil, A.: Basic number theory, Springer, 1967.

    Google Scholar 

  340. Hasse, H.: ‘Ueber die Darstellbarkeit von Zahlen durch quadratische Formen im Körper der rationalen Zahlen’, J. Reine Angew. Math. 152 (1923), 129–148.

    MATH  Google Scholar 

  341. Hasse, H.: ‘Ueber die Aequivalenz quadratischer Formen im Körper der rationalen Zahlen’, J. Reine Angew. Math. 152 (1923), 205–224.

    MATH  Google Scholar 

  342. Hasse, H.: ‘Symmetrische Matrizen im Körper der rationalen Zahlen’, J. Reine Angew. Math. 153 (1924), 12–43.

    Google Scholar 

  343. Hasse, H.: ‘Darstellbarkeit von Zahlen durch quadratische Formen in einem beliebigen algebraischen Zahlkörper’, J. Reine Angew. Math. 153 (1924), 113–130.

    MathSciNet  Google Scholar 

  344. Hasse, H.: ‘Aequivalenz quadratischer Formen in einem beliebigen algebraischen Zahlkörper’, J. Reine Angew. Math. 153 (1924), 158–162.

    MATH  Google Scholar 

  345. O’Meara, O.T.: Introduction to quadratic forms, Springer, 1963.

    Google Scholar 

  346. Lam, T.Y.: The algebraic theory of quadratic forms, Benjamin, 1973.

    Google Scholar 

  347. Cassels, J.W.S.: Rational quadratic forms, Acad. Press, 1978.

    Google Scholar 

  348. Hartshorne, R.: Algebraic geometry, Springer, 1977.

    Google Scholar 

  349. Manin, Yu.I.: ‘On the Hasse—Witt matrix of an algebraic curve’, Izv. Akad. Nauk. SSSR Ser. Mat. 25, no. 1 (1961), 153–172 (in Russian).

    MathSciNet  MATH  Google Scholar 

  350. Silverman, J.H.: The arithmetic of elliptic curves, Springer, 1986.

    Google Scholar 

  351. Hasse, H.: ‘Darstellbarkeit von Zahlen durch quadratische Formen in einem beliebigen algebraischen Zahlkörper’, J. Reine Angew. Math. 153 (1924), 113–130.

    MathSciNet  Google Scholar 

  352. Cassels, J.W.S. and Fröhlich, A. (eds.): Algebraic number theory, Acad. Press, 1967.

    Google Scholar 

  353. Cassels, J.W.S.: ‘Diophantine equations with special reference to elliptic curves’, J. London Math. Soc. 41 (1966), 193–291.

    MathSciNet  Google Scholar 

  354. Manin, Yu.N.: Cubic forms. Algebra, geometry, arithmetic, North-Holland, 1974 (translated from the Russian).

    Google Scholar 

  355. Serre, J.-P.: Cohomologie Galoisienne, Springer, 1964.

    Google Scholar 

  356. Chernusov, V.: The Hasse principle for groups of type E g, Minsk, 1988 (in Russian).

    Google Scholar 

  357. Rubin, K.: ‘Tate-Shafarevich groups and L-functions of ellip tic curves with complex multiplication’, Invent. Math. 89 (1987), 527–560.

    MathSciNet  MATH  Google Scholar 

  358. Kolyvagin, V.: The Mordell—Weil groups and the Shafarevich—Tate groups of Weil’s elliptic curves’, Izv. Akad Nauk. SSSR Ser. Mat. 52, no. 6 (1988).

    Google Scholar 

  359. Hausdorff, F.: Set theory, Chelsea, reprint, 1978 (translated from the German).

    Google Scholar 

  360. Arkhangel’skiĭ, A.V. and Ponomarev, V.l.: Fundamentals of general topology: problems and exercises, Reidel, 1984 (translated from the Russian).

    Google Scholar 

  361. Hausdorff, F.: ‘Dimension and äusseres Mass’, Math. Ann. 79 (1918), 157–179.

    MathSciNet  MATH  Google Scholar 

  362. Hurevicz, W. and Wallman, G.: Dimension theory, Princeton Univ. Press, 1948.

    Google Scholar 

  363. Falconer, K.J.: The geometry of fractal sets, Cambridge Univ. Press, 1985.

    Google Scholar 

  364. Hausdorff, F.: ‘Dimension and äusseres Mass’, Math. Ann. 79 (1918), 157–179.

    MathSciNet  MATH  Google Scholar 

  365. Dunford, N. and Schwartz, J.T.: Linear operators. General theory, 1, Interscience, 1958.

    Google Scholar 

  366. Carleson, L.: Selected problems on exceptional sets, v. Nostrand, 1967.

    Google Scholar 

  367. Dellacherie, C.: Ensembles analytiques, capacités, mesures de Hausdorff, Lecture notes in math., 295, Springer, 1972.

    Google Scholar 

  368. Falconer, K.J.: The geometry of fractal sets, Cambridge Univ. Press, 1985.

    Google Scholar 

  369. Federer, H.: Geometric measure theory, Springer, 1969.

    Google Scholar 

  370. Kahane, J.-P. and Salem, R.: Ensembles parfaits et séries trigonométriques, Hermann, 1963.

    Google Scholar 

  371. Gall, J.-F. le: Temps locaux d’intersection et points multiples des processus de Lévy’, in Sém. de Probab. XXI, Lecture notes in math., Vol. 1247, Springer, 1987, pp. 341-374.

    Google Scholar 

  372. Munroe, M.E.: Introduction to measure and integration, Addison-Wesley, 1953.

    Google Scholar 

  373. Rogers, C.A.: Hausdorff measures, Cambridge Univ. Press, 1970.

    Google Scholar 

  374. Chirka, E.M.: Complex analytic sets, Kluwer, 1989 (translated from the Russian).

    Google Scholar 

  375. Hausdorff, F.: Set theory, Chelsea, 1978 (translated from the German).

    Google Scholar 

  376. Urysohn, P.S.: Works on topology and other fields of mathematics, 2, Moscow-Leningrad, 1951 (in Russian).

    Google Scholar 

  377. Hausdorff, F.: Set theory, Chelsea, reprint, 1978 (translated from the German).

    Google Scholar 

  378. Arkhangel’skiĭ, A.V. and Ponomarev, V.I.: Fundamentals of general topology: problems and exercises, Reidel, 1984 (translated from the Russian).

    Google Scholar 

  379. Hausdorff, F.: ‘Summationsmethoden und Momentfolgen I, II’, Math. Z. 9 (1921), 74–109; 280-299.

    MathSciNet  MATH  Google Scholar 

  380. Hardy, G.H.: Divergent series, Clarendon, 1949.

    Google Scholar 

  381. Young, W.H.: ‘On the determination of the summability of a function by means of its Fourier constants’, Proc. London Math. Soc. (2) 12 (1913), 71–88.

    MATH  Google Scholar 

  382. Hausdorff, F.: ‘Eine Ausdehnung des ParseValschen Satzes über Fourierreihen’, Math. Z. 16 (1923), 163–169.

    MathSciNet  MATH  Google Scholar 

  383. Bary, N.K. [N.K. Bari]: A treatise on trigonometric series. Pergamon, 1964 (translated from the Russian).

    Google Scholar 

  384. Kaczmarz, S. and Steinhaus, H.: Theorie der Orthogonalreihen, Chelsea, reprint, 1951.

    Google Scholar 

  385. Zygmund, A.: Trigonometric series, 2, Cambridge Univ. Press, 1988.

    Google Scholar 

  386. Leeuw, K. de, Kahane, J.P. and Katznelson, Y.: ‘Sur les coefficients de Fourier des fonctions continues’, C.R. Acad. Sci. Paris 285 (1977), 1001–1003.

    MATH  Google Scholar 

  387. Kreĭn, S.G., Petunin, Yu.I. and Sevenov, E.M.: Interpolation of linear operators, Amer Math. Soc., 1982 (translated from the Russian).

    Google Scholar 

Download references

Authors
  1. V. I. Ponomarev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. B. Rudyak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. F. Kharshiladze
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yu. N. Subbotin
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. D. P. Zhelobenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. A. I. Shtern
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. B. I. Golubov
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. S. A. Rukova
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. E. D. Solomentsev
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. O. A. Ivanova
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. I. A. Aleksandrov
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. P. S. Soltan
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. V. I. Sobolev
    View author publications

    You can also search for this author in PubMed Google Scholar

  14. A. V. Prokhorov
    View author publications

    You can also search for this author in PubMed Google Scholar

  15. I. V. Dolgachev
    View author publications

    You can also search for this author in PubMed Google Scholar

  16. V. V. Rumyantsev
    View author publications

    You can also search for this author in PubMed Google Scholar

  17. I. B. Vapnyarskiĭ
    View author publications

    You can also search for this author in PubMed Google Scholar

  18. V. D. Mazurov
    View author publications

    You can also search for this author in PubMed Google Scholar

  19. V. M. Tikhomirov
    View author publications

    You can also search for this author in PubMed Google Scholar

  20. L. P. Kuptsov
    View author publications

    You can also search for this author in PubMed Google Scholar

  21. D. V. Anosov
    View author publications

    You can also search for this author in PubMed Google Scholar

  22. V. A. Yakubovich
    View author publications

    You can also search for this author in PubMed Google Scholar

  23. B. V. Khvedelidze
    View author publications

    You can also search for this author in PubMed Google Scholar

  24. S. V. Matveev
    View author publications

    You can also search for this author in PubMed Google Scholar

  25. P. I. Lizorkin
    View author publications

    You can also search for this author in PubMed Google Scholar

  26. S. V. Shvedenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  27. L. D. Kudryavtsev
    View author publications

    You can also search for this author in PubMed Google Scholar

  28. B. M. Bredikhin
    View author publications

    You can also search for this author in PubMed Google Scholar

  29. A. A. Konyushkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  30. Yu. A. Brychkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  31. A. P. Prudnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  32. E. M. Nikishin
    View author publications

    You can also search for this author in PubMed Google Scholar

  33. E. A. Gorin
    View author publications

    You can also search for this author in PubMed Google Scholar

  34. E. A. Grebennikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  35. A. B. Ivanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  36. A. L. Onishchik
    View author publications

    You can also search for this author in PubMed Google Scholar

  37. P. M. Tamrazov
    View author publications

    You can also search for this author in PubMed Google Scholar

  38. V. F. Emel’yanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  39. A. I. Barabanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  40. Yu. A. Rozanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  41. L. I. Kamynin
    View author publications

    You can also search for this author in PubMed Google Scholar

  42. V. A. Skvortsov
    View author publications

    You can also search for this author in PubMed Google Scholar

  43. E. M. Chirka
    View author publications

    You can also search for this author in PubMed Google Scholar

  44. E. B. Vinberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  45. Yu. G. Zarkhin
    View author publications

    You can also search for this author in PubMed Google Scholar

  46. I. G. Koshevnikova
    View author publications

    You can also search for this author in PubMed Google Scholar

  47. R. A. Minlos
    View author publications

    You can also search for this author in PubMed Google Scholar

  48. M. I. Voĭtsekhovskiĭ
    View author publications

    You can also search for this author in PubMed Google Scholar

  49. A. G. El’kin
    View author publications

    You can also search for this author in PubMed Google Scholar

  50. A. V. Arkhangel’skiĭ
    View author publications

    You can also search for this author in PubMed Google Scholar

  51. I. I. Volkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  52. E. M. Semenov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

M. Hazewinkel

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Ponomarev, V.I. et al. (1995). H. In: Hazewinkel, M. (eds) Encyclopaedia of Mathematics. Encyclopaedia of Mathematics, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3795-7_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4899-3795-7_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-7923-2974-9

  • Online ISBN: 978-1-4899-3795-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation