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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2019, Volume 161, Pages 104–129 (Mi into435)  

Asymptotic properties of entire functions with given laws of distribution of zeros

V. B. Sherstyukov

National Engineering Physics Institute "MEPhI", Moscow

Abstract: This review was compiled from the author's doctoral dissertation defended at the M. V. Lomonosov Moscow State University in February 2017. The authorТs results obtained in the last decade are systematized and summarized. The research relates to the classical direction of the theory of entire functions of one variable devoted to the connection between the asymptotic behavior of an entire function and the distribution of its zeros on the complex plane. The results presented are applied to the theory of complete and representing systems of exponents in spaces of analytic functions.

Keywords: canonical product, condensation index, entire function, type, indicator, upper and lower zero density, system of exponents, radius of completeness, representing system, decomposition into simple fractions

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00236_a
This work was supported by the Russian Foundation for Basic Research (project No. 18-01-00236).


Full text: PDF file (475 kB)
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Bibliographic databases:
UDC: 517.547
MSC: 30D15, 30D20

Citation: V. B. Sherstyukov, “Asymptotic properties of entire functions with given laws of distribution of zeros”, Complex Analysis. Entire Functions and Their Applications, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 161, VINITI, Moscow, 2019, 104–129

Citation in format AMSBIB
\Bibitem{She19}
\by V.~B.~Sherstyukov
\paper Asymptotic properties of entire functions with given laws of distribution of zeros
\inbook Complex Analysis. Entire Functions and Their Applications
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 161
\pages 104--129
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into435}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3975492}


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