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 Ufimsk. Mat. Zh., 2016, Volume 8, Issue 4, Pages 3–23 (Mi ufa348)

Representation of analytic functions

A. I. Abdulnagimova, A. S. Krivoshyevb

a Ufa State Aviation Technical University
b Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa

Abstract: In this paper we consider exponential series with complex exponents, whose real and imaginary parts are integer. We prove that each function analytical in the vicinity of the closure of a bounded convex domain in the complex plain can be expanded into the above mentioned series and this series converges absolutely inside this domain and uniformly on compact subsets. The result is based on constructing a regular subset with a prescribed angular density of the sequence of all complex numbers, whose real and imaginary parts are integer.

Keywords: analytic function, exponential series, regular set, density of sequence.

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English version:
Ufa Mathematical Journal, 2016, 8:4, 3–23 (PDF, 401 kB); https://doi.org/10.13108/2016-8-4-3

Bibliographic databases:

UDC: 517.5
MSC: 30D10

Citation: A. I. Abdulnagimov, A. S. Krivoshyev, “Representation of analytic functions”, Ufimsk. Mat. Zh., 8:4 (2016), 3–23; Ufa Math. J., 8:4 (2016), 3–23

Citation in format AMSBIB
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