Solvability of convolution equations in \(K_ M'\)
type: Item
instance of: scholarly article
title: Solvability of convolution equations in \(K_ M'\)
zbMATH Open document ID: 0661.46033
author: Saleh Abdullah
published in: Hokkaido Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: Let S be a convolution operator in the space of distributions \(K_ M'\) [\textit{I. M. Gel'fand} and \textit{G. E. Shilov}, Generalized functions, Vol. 3 (1967; Zbl 0133.375)]. Then a necessary and sufficient condition on S to have \(S*K_ M'=K_ M^{*'}\) is given. The main result in this paper gives the necessay and sufficient conditions for solvability of determined systems of convolution equations in \(K_ M'\). Three theorems are proved in this context. The author remarks that the main theorem of the paper [\textit{S. Sznajder} and \textit{Z. Zielezny}, Pac. J. Math. 3, No.2, 539-544 (1976; Zbl 0334.46043)] is extended by the first theorem of the above three theorems. Lastly the author feels that the question of finding the necessary and sufficient conditions for solvability of undetermined systems of convolution equations in \(K_ M'\) is yet to be solved.
Mathematics Subject Classification ID: 46F10
Mathematics Subject Classification ID: 44A35
Mathematics Subject Classification ID: 46A13
Mathematics Subject Classification ID: 46A11
zbMATH DE Number: 4080161
zbMATH Keywords: convolution operator in the space of distributions
zbMATH Keywords: solvability of determined systems of convolution equations
reviewed by: Gandikota L. N. Rao
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381517804
OpenAlex ID: W2081964567
DOI: 10.14492/HOKMJ/1381517804
description: scientific article; zbMATH DE number 4080161