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On Uniqueness Conditions for Entire Polyharmonic Functions

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Partial Differential and Integral Equations

Part of the book series: International Society for Analysis, Applications and Computation ((ISAA,volume 2))

Abstract

The main result of this paper is the answer — in the case of functions polyharmonic in the plane R 2 — to a uniqueness problem for poly- harmonic functions proposed recently by the well-known British mathematican W.K. Hayman [1]. Our reasoning is essentially based on the connection between polyharmonic functions of two real variables and polyanalytic functions of one complex variable [4].

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References

  1. Hayman, W.K. : A uniqueness problem for polyharmonic functions. In: Linear and Complex Analysis. Problem Book 3, Part II. Eds.:V.P.Havin, N.K.Nikolski. Lecture Notes in Mathematics 1574, Springer-Verlag, Berlin- Heidelberg, 1994, Problem 16. 16, pp. 326–327.

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  2. Hayman, W.K., Korenblum, B.: Representation and uniqueness theorems for polyharmonic functions. J. Anal. Math. 60 (1993), 113–133.

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  3. Hörmander, L. : Analysis of linear partial differential operators, 1. Springer- Verlag, Berlin-Heidelberg, 1981.

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  4. Balk, M.B. : Polyanalytic Functions. Mathematical Research 63. Akademie Verlag, Berlin, 1991.

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  5. Behnke, H., Thullen, P.: Theorie der Funktionen mehrerer komplexen Veränderlichen. Springer-Verlag, Berlin, 1934.

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  6. Ronkin, L.A. : Some topics on zero points distribution of entire functions of several variables. Mat. Sbornik 87 (1972), 351–368 (Russian).

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Author information

Authors and Affiliations

  1. Department of Mathematics, Smolensk Pedagogical Institute, Przhevalski str. 4, Smolensk, 214000, Russia

    M. B. Balk & M. Ya. Mazalov

Authors
  1. M. B. Balk
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  2. M. Ya. Mazalov
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Editor information

Editors and Affiliations

  1. Freie Universität Berlin, Berlin, Germany

    Heinrich G. W. Begehr

  2. University of Delaware, Newark, Delaware, USA

    Robert P. Gilbert

  3. Peking University, Beijing, China

    Guo-Chun Wen

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© 1999 Kluwer Academic Publishers

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Balk, M.B., Mazalov, M.Y. (1999). On Uniqueness Conditions for Entire Polyharmonic Functions. In: Begehr, H.G.W., Gilbert, R.P., Wen, GC. (eds) Partial Differential and Integral Equations. International Society for Analysis, Applications and Computation, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3276-3_16

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  • DOI: https://doi.org/10.1007/978-1-4613-3276-3_16

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3278-7

  • Online ISBN: 978-1-4613-3276-3

  • eBook Packages: Springer Book Archive

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