On spectral analysis of an integral-difference operator
type: Item
instance of: scholarly article
title: On spectral analysis of an integral-difference operator
zbMATH Open document ID: 0887.45001
DOI: 10.1023/A:1007481703103
author: J. Ning
published in: Letters in Mathematical Physics
publication date: 1998-01-14T00:00:00Z
review text: In the Hilbert space \(L_2 (\mathbb{R})\) the author considers the following integral operator \[ (K_{\chi_a} u)(x)= \int^\infty_{-\infty} {\chi_a (s)u(x) -\chi_a(x)u(s) \over |x-s|} ds, \] where \(\chi_a(x)\) is the indicator of the interval \([-a,a]\); such an operator arises as a collision operator in statistical physics models. He gives a complete spectral description for the operator \(K_{\chi_a}\) and for the restricted operator \(\chi_a K_{\chi_a} \chi_a\) acting in the space \(L_2 (-a,a)\).
Mathematics Subject Classification ID: 45C05
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 45P05
zbMATH DE Number: 1104157
zbMATH Keywords: integral-difference operator
zbMATH Keywords: spectrum
reviewed by: N. Karapetiants
MaRDI profile type: Publication
full work available at URL: a:1007481703103
OpenAlex ID: W83199254
description: scientific article; zbMATH DE number 1104157