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Ukrainian Mathematical Journal

, Volume 46, Issue 8, pp 1188–1192 | Cite as

Approximation of functions subharmonic in a disk by the logarithm of the modulus of an analytic function

  • M. A. Girnyk
Brief Communications

Abstract

Yulmukhametov's result concerning the approximation of a function subharmonic in a bounded domain by the logarithm of the modulus of an analytic function is supplemented with an estimate of the exceptional set in the important case of a disk. We show that this approximation is unimprovable in a certain sense.

Keywords

Analytic Function Bounded Domain Important Case 
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References

  1. 1.
    W. K. Hayman and P. B. Kennedy,Subharmonic Functions [Russian translation], Mir, Moscow (1980).Google Scholar
  2. 2.
    R. S. Yulmukhametov, “Approximation of subharmonic functions,”Anal Math.,11, No. 3, 257–282 (1985).Google Scholar
  3. 3.
    N. S. Landkof,Foundations of Modern Potential Theory [in Russian], Nauka, Moscow (1966).Google Scholar
  4. 4.
    A. A. Gol'dberg and I. V. Ostrovskii,Distribution of Values of Meromorphic Functions [in Russian], Nauka, Moscow (1970).Google Scholar
  5. 5.
    M. A. Lavrent'ev and B. V. Shabat,Methods of the Theory of Functions of Complex Variable [in Russian], Nauka, Moscow (1973).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • M. A. Girnyk
    • 1
  1. 1.Lvov Trade InstituteLvov

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