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.
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; J. Math. Sci., 250:3 (2020), 419–453
\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}
\transl
\jour J. Math. Sci.
\yr 2020
\vol 250
\issue 3
\pages 419--453
\crossref{https://doi.org/10.1007/s10958-020-05024-4}
Linking options:
https://www.mathnet.ru/eng/fpm1781
https://www.mathnet.ru/eng/fpm/v22/i1/p51
This publication is cited in the following 9 articles:
G. G. Braichev, “Zadacha Silvestra i mnozhestva edinstvennosti v klassakh tselykh funktsii”, Funktsionalnye prostranstva. Differentsialnye operatory. Problemy
matematicheskogo obrazovaniya, SMFN, 70, no. 1, Rossiiskii universitet druzhby narodov, M., 2024, 25–37
A. Yu. Popov, V. B. Sherstyukov, “Otsenka snizu v srednem minimuma modulya na okruzhnostyakh dlya tseloi funktsii nulevogo roda”, Funktsionalnye prostranstva. Differentsialnye operatory. Problemy
matematicheskogo obrazovaniya, SMFN, 70, no. 1, Rossiiskii universitet druzhby narodov, M., 2024, 150–162
G. G. Braichev, V. B. Sherstyukov, “Uniqueness Theorem for Entire Functions of Exponential Type”, Lobachevskii J Math, 45:6 (2024), 2672
G. G. Braichev, “On the Connection between the Growth of Zeros and the Decrease of Taylor Coefficients of Entire Functions”, Math. Notes, 113:1 (2023), 27–38
G. G. Braichev, B. N. Khabibullin, V. B. Sherstyukov, “Sylvester problem, coverings by shifts, and uniqueness theorems for entire functions”, Ufa Math. J., 15:4 (2023), 31–41
G. G. Braichev, O. V. Sherstyukova, “On least type of entire function with given subsequence of zeros”, Ufa Math. J., 14:3 (2022), 17–21
N. S. Imanbaev, “On nonlocal perturbation of the problem on eigenvalues of differentiation operator on a segment”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 31:2 (2021), 186–193
G. G. Braichev, “On the Lower Indicator of an Entire Function
with Roots of Zero Lower Density Lying on a Ray”, Math. Notes, 107:6 (2020), 907–919
G. G. Braichev, V. B. Sherstyukov, “Otsenki indikatorov tseloi funktsii s otritsatelnymi kornyami”, Vladikavk. matem. zhurn., 22:3 (2020), 30–46
Citation in format AMSBIB
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