Skip to main content
Log in

On one criterion for analyticity of functions

Ukrainian Mathematical Journal Aims and scope

Abstract

We prove a generalization of the well-known Dzyadyk theorem that gives an interesting geometric criterion for the analyticity of functions.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. K. Dzyadyk, “Geometric definition of analytic functions,” Usp. Mat. Nauk, 15, No. 1, 191–194 (1960).

    Google Scholar 

  2. A. Goodman, “On a characterization of analytic function,” Amer. Math. Monthly, 71, No. 3, 265–267 (1964).

    Article  MATH  MathSciNet  Google Scholar 

  3. Yu. Yu. Trokhimchuk and V. M. Safonov, “On one criterion for the constancy of a complex function,” Ukr. Mat. Zh., 1, No. 8, 1096–1104 (1999).

    Article  MathSciNet  Google Scholar 

  4. S. Stoilow, Teoria Functilor de o Variabila Complexa, Editura Academiei Republicii Populare Romane (1954).

  5. Yu. Yu. Trokhimchuk, Removable Singularities of Analytic Functions [in Russian], Naukova Dumka, Kiev (1992).

    Google Scholar 

  6. H. Federer, Geometric Measure Theory, Springer, New York (1969).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1410–1418, October, 2007.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Trokhimchuk, Y.Y. On one criterion for analyticity of functions. Ukr Math J 59, 1581–1590 (2007). https://doi.org/10.1007/s11253-008-0008-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-008-0008-9

Keywords

Navigation