Solvability of convolution equations in the Beurling spaces of ultradifferentiable functions of mean type on an interval
type: Item
instance of: scholarly article
title: Solvability of convolution equations in the Beurling spaces of ultradifferentiable functions of mean type on an interval
zbMATH Open document ID: 1278.46036
DOI: 10.1134/S0037446612020206
author: D. A. Abanina
published in: Siberian Mathematical Journal
publication date: 2012-11-14T00:00:00Z
review text: A convolution equation is considered in the Beurling space of ultradifferentiable functions of mean type on an interval. The author completely describes conditions under which the convolution equation has a solution. As a particular case, infinite-order differential equations with constant coefficients are considered. Necessary and sufficient conditions of solvability of such equations are established. Some examples illustrate the theory.
reviewed by: Sergii Sharyn
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 46E10
Mathematics Subject Classification ID: 44A35
Mathematics Subject Classification ID: 34A35
zbMATH DE Number: 6105689
zbMATH Keywords: Beurling type ultradifferentiable functions
zbMATH Keywords: convolution equation
zbMATH Keywords: convolution operator
zbMATH Keywords: weight function
zbMATH Keywords: division theorem
MaRDI profile type: Publication
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full work available at URL: s0037446612020206
OpenAlex ID: W2016690365
description: scientific article; zbMATH DE number 6105689