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Regularly distributed subsets in the complex plane


Authors: A. I. Abdulnagimov and A. S. Krivosheyev
Translated by: N. N. Osipov
Original publication: Algebra i Analiz, tom 28 (2016), nomer 4.
Journal: St. Petersburg Math. J. 28 (2017), 433-464
MSC (2010): Primary 30D20
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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Additional Information

A. I. Abdulnagimov
Affiliation: Institute of mathematics with computer center, Ufa scientific center Russian Academy of Sciences, Chernyshevskiĭ str. 112, 450048 Ufa, Russia
Email: buffonishe@mail.ru

A. S. Krivosheyev
Affiliation: Bashkir State University, Zaki Validi str. 32, 450076 Ufa, Russia
Email: kriolesya2006@yandex.ru

DOI: https://doi.org/10.1090/spmj/1458
Keywords: Regularly distributed set, series of exponential functions, entire function, convex domain
Received by editor(s): June 25, 2015
Published electronically: May 4, 2017
Article copyright: © Copyright 2017 American Mathematical Society