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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 162, Pages 15–24
(Mi into437)
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This article is cited in 2 scientific papers (total in 2 papers)
Behavior of coefficients of series of exponents of finite order near the boundary
A. M. Gaisinab, G. A. Gaisinab a Institute of Mathematics with Computing Centre — Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa
b Bashkir State University, Ufa
Abstract:
Let $G$ be a bounded convex domain with a smooth boundary in which a given system of exponents is not complete. For a class of analytic functions in $G$ that can be represented in $G$ by a series of exponents, we examine the behavior of coefficients of the series expansion in terms of the growth order near the boundary $\partial G$. We establish two-sided estimates for the order through characteristics depending only on the indices of the series of exponents and the supporting function of the domain (these estimates are strong). As a consequence, we obtain a formula for calculating the growth order through the coefficients.
Keywords:
series of exponents, domain with smooth boundary, behavior near the boundary, order, $R$-order.
Citation:
A. M. Gaisin, G. A. Gaisina, “Behavior of coefficients of series of exponents of finite order near the boundary”, Complex Analysis. Mathematical Physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 162, VINITI, Moscow, 2019, 15–24
Linking options:
https://www.mathnet.ru/eng/into437 https://www.mathnet.ru/eng/into/v162/p15
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Abstract page: | 176 | Full-text PDF : | 60 | References: | 39 | First page: | 8 |
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