Convolution equations on spaces of quasi-nuclear functions of a given type and order
type: Item
instance of: scholarly article
title: Convolution equations on spaces of quasi-nuclear functions of a given type and order
zbMATH Open document ID: 1211.46038
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2010-10-12T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1284570737
review text: This nice paper is a kind of continuation of the author's paper [Port.\ Math.\ (N.\,S.) 65, No.\,2, 285--309 (2008; Zbl 1152.46033)]. The author proves existence and approximation results for convolution equations on the spaces of \((s;(r,q))\)-quasi-nuclear mappings of a given type and order on a Banach space \(E\). The results of the paper generalize previous works of \textit{C.\,Gupta, B.\,Malgrange, M.\,C.\thinspace Matos} and \textit{A.\,Martineau} [Bull.\ Soc.\ Math.\ Fr.\ 95, 109--154 (1967; Zbl 0167.44202)] related to partial differential equations with constant coefficients for entire functions.
Mathematics Subject Classification ID: 46G25
Mathematics Subject Classification ID: 46G20
Mathematics Subject Classification ID: 46N20
zbMATH DE Number: 5798748
zbMATH Keywords: convolution equations
zbMATH Keywords: partial differential equations
zbMATH Keywords: Banach spaces
zbMATH Keywords: homogeneous polynomials
zbMATH Keywords: division theorems
zbMATH Keywords: quasi-nuclear mappings
author: V. V. Fávaro
reviewed by: Daniel Pellegrino
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5798748