Abstract
We prove a generalization of the well-known Dzyadyk theorem that gives an interesting geometric criterion for the analyticity of functions.
Similar content being viewed by others
References
V. K. Dzyadyk, “Geometric definition of analytic functions,” Usp. Mat. Nauk, 15, No. 1, 191–194 (1960).
A. Goodman, “On a characterization of analytic function,” Amer. Math. Monthly, 71, No. 3, 265–267 (1964).
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).
S. Stoilow, Teoria Functilor de o Variabila Complexa, Editura Academiei Republicii Populare Romane (1954).
Yu. Yu. Trokhimchuk, Removable Singularities of Analytic Functions [in Russian], Naukova Dumka, Kiev (1992).
H. Federer, Geometric Measure Theory, Springer, New York (1969).
Author information
Authors and Affiliations
Additional information
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1410–1418, October, 2007.
Rights 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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-008-0008-9