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 Fundam. Prikl. Mat., 2018, Volume 22, Issue 1, Pages 51–97 (Mi fpm1781)

Sharp bounds for asymptotic characteristics of growth of entire functions with zeros on given sets

G. G. Braicheva, V. B. Sherstyukovb

a Moscow State Pedagogical University
b National Engineering Physics Institute "MEPhI", Moscow

Abstract: The paper provides an overview of the latest research on the two-sided estimates of classical characteristics of growth of entire functions such as the type and the lower type in terms of the ordinary or average densities of the distribution of zeros. We give also the accurate estimates of the type of an entire function, taking into account additionally the step and the lacunarity index of the sequence of zeros. The results under consideration are based on the solution of extremal problems in classes of entire functions with restrictions on the behavior of the zero set. Particular attention is paid to the following important cases of the location of zeros: on a ray, on a straight line, on a number of rays, in the angle, or arbitrarily in the complex plane.

 Funding Agency Grant Number Russian Foundation for Basic Research 18-01-00236_a

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UDC: 517.547.22

Citation: G. G. Braichev, V. B. Sherstyukov, “Sharp bounds for asymptotic characteristics of growth of entire functions with zeros on given sets”, Fundam. Prikl. Mat., 22:1 (2018), 51–97

Citation in format AMSBIB
\Bibitem{BraShe18} \by G.~G.~Braichev, V.~B.~Sherstyukov \paper Sharp bounds for asymptotic characteristics of growth of entire functions with zeros on given sets \jour Fundam. Prikl. Mat. \yr 2018 \vol 22 \issue 1 \pages 51--97 \mathnet{http://mi.mathnet.ru/fpm1781}