Spectral analysis of difference operators with strongly continuous coefficients
type: Item
instance of: scholarly article
title: Spectral analysis of difference operators with strongly continuous coefficients
zbMATH Open document ID: 0924.47022
published in: Russian Mathematics
publication date: 1999-04-27T00:00:00Z
review text: Let \(G\) be a locally compact abelian group, \(X\) be a Banach space and \({\mathcal F}(G,X)\) be the set of measurable functions with values in \(X.\) The author considers difference operators \(\mathcal D\) of the form \(({\mathcal D}x)(g)=\sum A_n (g)x(g+g_n),\) where \(x\in {\mathcal F}(G,X)\), \(g, g_n\in G\) and the \(A_n(g)\) are strongly continuous functions on \(G\) with values in \(\text{End} X.\) The structure of the inverse operator to \(\mathcal D\) is studied. In particular spectral properties of the operator of weighted translation, i.e. \(({\mathcal D}x)(g)=A(g)x(g+g_0)\) are examined. An application to first order linear differential operators is given.
Mathematics Subject Classification ID: 47B39
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 1256806
zbMATH Keywords: difference operators
zbMATH Keywords: spectral properties
zbMATH Keywords: weighted translation
zbMATH Keywords: first-order linear-differential operators
author: Anatoly G. Baskakov
reviewed by: Ryszard Szwarc
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1256806