Representation of analytic functions in a closed polydomain by Dirichlet series
type: Item
instance of: scholarly article
title: Representation of analytic functions in a closed polydomain by Dirichlet series
zbMATH Open document ID: 0667.32004
DOI: 10.1007/BF00969744
published in: Siberian Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: In the paper, a generalization of the results of \textit{A. F. Leont'ev} [Izv. Akad. Nauk SSSR, Ser. Mat. 37, 577-592 (1973; Zbl 0275.30004)] on representations of analytic functions in closed convex domains in \({\mathbb{C}}\) by Dirichlet series to the case of several complex variables is given. There are given necessary and sufficient conditions in order that, for any analytic function f in a polydomain \(D=D_ 1\times...\times D_ n\subset {\mathbb{C}}^ n,\) where \(D_ i\) are convex domains in the complex plane, and having the \(C^ 2\)-extension to \(\bar D\) with respect to each variable, the Dirichlet series corresponding to f (depending on some auxiliary entire functions connected with D) be absolutely convergent in \(\bar D,\) uniformly convergent in \(\bar D,\) convergent to f in \(\bar D,\) respectively. The conditions are given in terms of the above entire functions connected with D.
Mathematics Subject Classification ID: 32A10
Mathematics Subject Classification ID: 32A07
Mathematics Subject Classification ID: 32A30
Mathematics Subject Classification ID: 30B50
zbMATH DE Number: 4091849
zbMATH Keywords: representations of analytic functions
zbMATH Keywords: Dirichlet series
zbMATH Keywords: polydomain
zbMATH Keywords: entire functions
author: Gafurjan I. Ibragimov
reviewed by: Tadeusz Krasiński
MaRDI profile type: Publication
cites work: On the representation of functions by Dirichlet double series
cites work: Q4109902
full work available at URL: https://doi.org/10.1007/bf00969744
OpenAlex ID: W2083139918
description: scientific article; zbMATH DE number 4091849