On the equations \(Ax=q\) and \(SX-XT=Q\)
type: Item
instance of: scholarly article
title: On the equations \(Ax=q\) and \(SX-XT=Q\)
zbMATH Open document ID: 0647.47028
DOI: 10.1016/0022-1236(88)90092-4
author: S. H. Smith
published in: Journal of Functional Analysis
publication date: 1988-01-01T00:00:00Z
review text: Let A be the generator of a certain semigroup, the authors prove the existence of a unique solution x of \(Ax=q\). About this, three equivalent characterizing conditions are demonstrated. This result is applied to study the solvability of the operator euqation \[ (*)\quad SX-XT=Q, \] where S and -T are generators of some semigroups of operators. Three equivalent statements are given for the existence of a solution of (*). These results generalize existence theorems of several authors.
Mathematics Subject Classification ID: 47A62
Mathematics Subject Classification ID: 47A50
zbMATH DE Number: 4056370
zbMATH Keywords: existence theorems
reviewed by: Walter Petry
MaRDI profile type: Publication
full work available at URL: 0022-1236(88)90092-4
OpenAlex ID: W1998212391
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description: scientific article; zbMATH DE number 4056370