Spectral analysis for a class of integral-difference operators: known facts, new results, and open problems
type: Item
instance of: scholarly article
title: Spectral analysis for a class of integral-difference operators: known facts, new results, and open problems
zbMATH Open document ID: 1084.47040
DOI: 10.1155/S1026022604401022
published in: Discrete Dynamics in Nature and Society
publication date: 2005-03-21T00:00:00Z
full work available at URL: https://eudml.org/doc/125788
review text: The author presents a review of the existing literature on the spectral analysis of integral-difference operators of the form \[ {\mathcal K}_\phi:u(x)\mapsto \int_\infty^\infty \frac{u(x)\phi (s)-u(s)\phi (x)}{| x-s| }ds \] acting on \(L_2({\mathbb R},dx)\), where \(\phi(x)\) is a probability function on \(\mathbb R\). These operators appear in some non-equilibriun statistical physics models as collision operators.
reviewed by: Chandra Shekhar Sharma
Mathematics Subject Classification ID: 47G20
Mathematics Subject Classification ID: 47N55
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 82C99
zbMATH DE Number: 2148592
zbMATH Keywords: spectral analysis
zbMATH Keywords: integral-difference operators
zbMATH Keywords: nonequilibrium statistical mechanics
author: Yu. B. Mel'nikov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2148592