Regularly distributed subsets in the complex plane

Abdulnagimov, A.; Krivosheyev, A.

doi:10.1090/spmj/1458

Regularly distributed subsets in the complex plane
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by A. I. Abdulnagimov and A. S. Krivosheyev
Translated by: N. N. Osipov

St. Petersburg Math. J. 28 (2017), 433-464

DOI: https://doi.org/10.1090/spmj/1458

Published electronically: May 4, 2017

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Abstract:

Certain conditions are studied under which there exists a regularly distributed set that is a part of a given sequence of complex numbers and, moreover, contains a given subsequence of that sequence. On this basis, splitting of entire functions and their asymptotic behavior are investigated. The results are also applied to problems concerning the completeness of systems of exponential monomials in convex domains and the representation of functions analytic on compact convex sets, as well as to the fundamental principle problem for invariant subspaces of functions.

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