Skip to main content
SpringerLink
Log in

Tauber-Sätze für Potenzreihenverfahren

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literaturverzeichnis

  1. S. Aljancić andD. Arandelović,O-regularly varying functions. Publ. Inst. Math. (Beograd) (N.S.) (36)22, 5–22 (1977).

    Google Scholar 

  2. D. Borwein, Tauberian conditions for the equivalence of weighted mean and power series methods of summability. Canad. Math. Bull.24, 309–316 (1981).

    Google Scholar 

  3. D. Borwein andA. Meir, A Tauberian theorem concerning weighted means and power series. Math. Proc. Cambridge Philos. Soc.101, 283–286 (1987).

    Google Scholar 

  4. D. Gaier, Gap theorems for logarithmic summability. Analysis1, 9–24 (1981).

    Google Scholar 

  5. L. de Haan, Note on a paper by H. G.Tucker. Ann. Math. Statist.41, 729–732 (1970).

    Google Scholar 

  6. G. H. Hardy andJ. E. Littlewood, Tauberian theorems concerning power series and Dirichlet's series whose coefficients are positive. Proc. London Math. Soc. (2)13, 174–191 (1914).

    Google Scholar 

  7. G. H. Hardy andJ. E. Littlewood, A further note on the converse of Abel's theorem. Proc. London Math. Soc. (2)25, 219–236 (1926).

    Google Scholar 

  8. K. Ishiguro, A converse theorem on the summability methods. Proc. Japan Acad.39, 38–41 (1963).

    Google Scholar 

  9. K. Ishiguro, Tauberian theorems concerning the summability methods of logarithmic type. Proc. Japan Acad.39, 156–159 (1963).

    Google Scholar 

  10. K. Ishiguro, A Tauberian theorem for (J, p n) summability. Proc. Japan Acad.40, 807–812 (1964).

    Google Scholar 

  11. K. Ishiguro, Two Tauberian theorems for (J, p n) summability. Proc. Japan Acad.41, 40–45 (1965).

    Google Scholar 

  12. A. Jakimovski, W. Meyer-König andK. Zeller, Power series methods of summability: Positivity and gap perfectness. Trans. Amer. Math. Soc.266, 309–317 (1981).

    Google Scholar 

  13. A. Jakimovski andH. Tietz, Regularly varying functions and power series methods. J. Math. Anal. Appl.73, 65–84 (1980). Errata ibid.95, 597–598 (1983).

    Google Scholar 

  14. J. Karamata, Neuer Beweis und Verallgemeinerung einiger Tauberian-Sätze. Math. Z.33, 294–299 (1931).

    Google Scholar 

  15. J. Karamata, Neuer Beweis und Verallgemeinerung der Tauberschen Sätze, welche die Laplacesche und Stieltjessche Transformation betreffen. J. Reine Angew. Math.164, 27–39 (1931).

    Google Scholar 

  16. B. H. Korenblyum, On the asymptotic behaviour of Laplace integrals near the boundary of a region of convergence. Dokl. Akad. Nauk. SSSR (N.S.)104, 173–176 (1955).

    Google Scholar 

  17. V. K. Krishnan, Gap Tauberian theorem for generalized Abel summability. Math. Proc. Cambridge Philos. Soc.78, 497–500 (1975).

    Google Scholar 

  18. V. K. Krishnan, Gap Tauberian theorem for logarithmic summability (L). Quart. J. Math. Oxford (2)30, 77–87 (1979).

    Google Scholar 

  19. B. Kwee, On generalized logarithmic methods of summation. J. Math. Anal. Appl.35, 83–89 (1971).

    Google Scholar 

  20. J. E. Littlewood, The converse of Abel's theorem on power series. Proc. London Math. Soc. (2)9, 434–448 (1911).

    Google Scholar 

  21. W. Meyer-König undH. Tietz, Über Umkehrbedingungen in der Limitierungstheorie. Arch. Math. (Brno)5, 177–186 (1969).

    Google Scholar 

  22. G. A. Mikhalin, Theorems of Tauberian type for (J, p n) summation methods. Ukrain. Mat. Zh.29, 763–770 (1977). English translation: Ukrainian Math. J.29, 564–569 (1977).

    Google Scholar 

  23. G. A. Mikhalin, On conditions for equivalence of the (¯R, p n) and (J, p n) summation methods. Izv. Vysš. Učebn. Zaved. Matematika 1979, no. 5, 41–51. English translation: Soviet Math. (Iz. VUZ) (5)23, 39–48 (1979).

    Google Scholar 

  24. G. A. Mikhalin, Generalization of Tauberian theorems for a class of (J, p n)-summability. Izv. Vysš. Učebn. Zaved. Matematika 1980. no. 4, 61–68. English translation: Soviet Math. (Iz. VUZ) (4)24, 69–76 (1980).

    Google Scholar 

  25. R. Phillips, A Tauberian theorem for a scale of logarithmic methods of summation. Canad. J. Math.25, 897–902 (1973).

    Google Scholar 

  26. M. S. Rangachari andY. Sitaraman, Tauberian theorems for logarithmic summability (L). Tôhoku Math. J. (2)16, 257–269 (1964). Correction ibid.17, 443 (1965).

    Google Scholar 

  27. E.Seneta, Regularly varying functions, Berlin-Heidelberg-New York 1976.

  28. K. Soni, Slowly varying functions and generalized logarithmic summability. J. Math. Anal. Appl.53, 692–703 (1976).

    Google Scholar 

  29. U. Stadtmüller andR. Trautner, Tauberian theorems for Laplace transforms. J. Reine Angew. Math.311/312, 283–290 (1979).

    Google Scholar 

  30. U. Stadtmüller andR. Trautner, Ratio Tauberian theorems for Laplace transforms without monotonicity assumptions. Quart. J. Math. Oxford (2)36, 363–381 (1985).

    Google Scholar 

  31. F. Štěpánek, A Tauber's theorem for (J, p n) summability. Monatsh. Math.70, 256–260 (1966).

    Google Scholar 

  32. K.Zeller und W.Beekmann, Theorie der Limitierungsverfahren, Berlin-Heidelberg-New York 1970.

Download references

Author information

Author notes

  1. Hubert Tietz

    Present address: Mathematisches Institut A, Universität Stuttgart, Pfaffenwaldring 57, D-7000, Stuttgart 80

  2. Rolf Trautner

    Present address: Abteilung für Mathematik, Universität Ulm, Oberer Eselsberg, D-7900, Ulm

Authors and Affiliations

    Authors
    1. Hubert Tietz
      View author publications

      You can also search for this author in PubMed Google Scholar

    2. Rolf Trautner
      View author publications

      You can also search for this author in PubMed Google Scholar

    Additional information

    Herrn W. Meyer-König zum 75. Geburtstag gewidmet

    Rights and permissions

    Reprints and permissions

    About this article

    Cite this article

    Tietz, H., Trautner, R. Tauber-Sätze für Potenzreihenverfahren. Arch. Math 50, 164–174 (1988). https://doi.org/10.1007/BF01194575

    Download citation

    • Received:

    • Issue Date:

    • DOI: https://doi.org/10.1007/BF01194575

    Search

    Navigation