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Harmonic wavelets in boundary value problems for harmonic and biharmonic functions

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Abstract

We consider boundary value problems in a disk and in a ring for homogeneous equations with the Laplace operator of the first and second orders. Solutions are represented in terms of bases of harmonic wavelets in Hardy spaces of harmonic functions in a disk and in a ring, which were constructed earlier.

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References

  1. Yu. N. Subbotin and N. I. Chernykh, Proc. Internat. Stechkin Summer School on Function Theory (Izd. Tul’sk. Gos. Univ., Tula, 2007), pp. 129–149 [in Russian].

    Google Scholar 

  2. Y. Meyer, Ondelettes et Opérateurs (Hermann, Paris, 1990).

    Google Scholar 

  3. D. Offin and K. Oskolkov, Constr. Approx. 9, 319 (1963).

    Article  MathSciNet  Google Scholar 

  4. Yu. N. Subbotin and N. I. Chernykh, Izv. Ross. Akad. Nauk, Ser. Mat. 64(1), 145 (2000).

    MathSciNet  Google Scholar 

  5. M. A. Lavrent’ev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable (Nauka, Moscow, 1965) [in Russian].

    Google Scholar 

  6. A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics (Nauka, Moscow, 1966; Dover, New York, 1990).

    Google Scholar 

  7. A. Zygmund, Trigonometric Series (Cambridge Univ. Press, 1959; Mir, Moscow, 1965), Vol. 1 [in Russian].

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia

    Yu. N. Subbotin & N. I. Chernykh

Authors
  1. Yu. N. Subbotin
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  2. N. I. Chernykh
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Corresponding author

Correspondence to Yu. N. Subbotin.

Additional information

Original Russian Text © Yu.N. Subbotin, N.I. Chernykh, 2010, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2010, Vol. 16, No. 4.

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Subbotin, Y.N., Chernykh, N.I. Harmonic wavelets in boundary value problems for harmonic and biharmonic functions. Proc. Steklov Inst. Math. 273 (Suppl 1), 142–159 (2011). https://doi.org/10.1134/S0081543811050154

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  • DOI: https://doi.org/10.1134/S0081543811050154

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