The order of growth of an exponential series near the boundary of the convergence domain

IF 0.7 4区数学 Q2 MATHEMATICS St Petersburg Mathematical Journal Pub Date : 2022-05-05 DOI:10.1090/spmj/1708

G. Gaisina

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引用次数: 0

Abstract

For a class of analytic functions in a bounded convex domain G G that admit an exponential series expansion in D D , the behavior of the coefficients of this expansion is studied in terms of the growth order near the boundary ∂ G \partial G . In the case where G G has a smooth boundary, unimprovable two-sided estimates are established for the order via characteristics depending only on the exponents of the exponential series and the support function of G G . As a consequence, a formula is obtained for the growth of the exponential series via the coefficients and the support function of the convergence domain G G .

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收敛域边界附近指数级数的增长阶

对于在有界凸域G G中允许在D D中进行指数级数展开的一类分析函数，该展开的系数的行为是根据边界附近的增长阶数来研究的。在G G具有光滑边界的情况下，通过仅依赖于指数级数的指数和G G的支持函数的特性，对阶建立了不可改进的双侧估计。因此，通过收敛域G G的系数和支持函数，得到了指数级数增长的公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

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