Geodesic
Representation of analytic functions
Ufa mathematical journal, Tome 8 (2016) no. 4, pp. 3-23

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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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     author = {A. I. Abdulnagimov and A. S. Krivoshyev},
     title = {Representation of analytic functions},
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A. I. Abdulnagimov; A. S. Krivoshyev. Representation of analytic functions. Ufa mathematical journal, Tome 8 (2016) no. 4, pp. 3-23. http://geodesic.mathdoc.fr/item/UFA_2016_8_4_a0/