Behavior of Coefficients of Series of Exponentials of Finite Order Near the Boundary

Autor:	G. A. Gaisina, A. M. Gaisin
Rok vydání:	2021
Předmět:	Statistics and Probability Series (mathematics) Applied Mathematics General Mathematics Bounded function Mathematical analysis Boundary (topology) Support function Series expansion Domain (mathematical analysis) Mathematics Analytic function Exponential function
Zdroj:	Journal of Mathematical Sciences. 257:286-295
ISSN:	1573-8795 1072-3374
DOI:	10.1007/s10958-021-05482-4
Popis:	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 exponentials, we examine the behavior of coefficients of the series expansion in terms of the growth order near the boundary ∂G. We establish two-sided estimates for the order through characteristics depending only on the indices of the series of exponentials and the support function of the domain (these estimates are strong). As a consequence, we obtain a formula for calculating the growth order through the coefficients.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::427a93dc0b1fa6bd8c83e2708a97f628 https://doi.org/10.1007/s10958-021-05482-4 Zobrazit plný text záznamu Plný text ve formátu PDF