Geodesic
Properly distributed subsequence on the line
Ufa mathematical journal, Tome 7 (2015) no. 1, pp. 3-12

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In the article we consider first order sequences of complex numbers. We prove that a sequence of nonzero minimal density contains a subsequence of the same density. We also prove that a real sequence of nonzero minimal density contains a properly distributed subsequence. Basing on this fact, we prove a result on representation of an entire function of exponential type with real zeros as a product of two entire functions with the same properties. Moreover, one of these functions has a regular growth. As a corollary, we obtain a result on completeness of exponential systems with real exponents in the space of analytic functions in a bounded convex domain of the complex plane.
Keywords: entire function, regular growth, zero set. 
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A. I. Abdulnagimov; A. S. Krivoshyev. Properly distributed subsequence on the line. Ufa mathematical journal, Tome 7 (2015) no. 1, pp. 3-12. http://geodesic.mathdoc.fr/item/UFA_2015_7_1_a0/