Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 162, Pages 15–24 (Mi into437)  

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
Full-text PDF (227 kB) Citations (2)
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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.
Bibliographic databases:
Document Type: Article
UDC: 517.537.7
MSC: 30D10
Language: Russian
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
Citation in format AMSBIB
\Bibitem{GaiGai19}
\by A.~M.~Gaisin, G.~A.~Gaisina
\paper Behavior of coefficients of series of exponents of finite order near the boundary
\inbook Complex Analysis. Mathematical Physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 162
\pages 15--24
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into437}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3981813}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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    Abstract page:176
    Full-text PDF :60
    References:39
    First page:8
     
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