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Ukrainian Mathematical Journal

, Volume 45, Issue 8, pp 1171–1177 | Cite as

Pseudoanalyticity of continuous functions with the σ-preservation of angles

  • A. V. Bondar'
  • E. A. Luk'yanova
Article
  • 19 Downloads

Abstract

The following theorem is proved: Every continuous function satisfying the conditionK σ is pseudo-analytic. The conditionK σ is a generalization of the Men'shov condition, well known in the theory of analytic functions.

Keywords

Continuous Function Analytic Function 
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References

  1. 1.
    A. V. Bondar' and E. A. Luk'yanova, “On the structure of the sets of σ-monogeneity for continuous functions,”Ukr. Mat. Zh.,45, No. 2, 226–232 (1993).Google Scholar
  2. 2.
    A. V. Bondar' and E. A. Luk'yanova, “On pseudoanalyticity of continuous functions with constant σ-expansion,”Ukr. Mat. Zh.,45, No. 4, 459–465 (1993).Google Scholar
  3. 3.
    Yu. Yu. Trokhimchuk,Continuous Maps and Monogeneity Conditions [in Russian], Fizmatgiz, Moscow (1963).Google Scholar
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    I. N. Vekua,Generalized Analytic F unctions, [in Russian], Fizmatgiz, Moscow (1959).Google Scholar
  5. 5.
    G. N. Polozhii,Generalization of the Theory of Analytic Functions of a Complex Variable [in Russian], Kiev University, Kiev (1965).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • A. V. Bondar'
    • 1
  • E. A. Luk'yanova
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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