Spectra and dynamics of bounded pseudo-differential operators
type: Item
instance of: scholarly article
title: Spectra and dynamics of bounded pseudo-differential operators
zbMATH Open document ID: 0897.35085
published in: Osaka Journal of Mathematics
publication date: 1998-03-25T00:00:00Z
review text: The author studies the spectral properties of the pseudodifferential operator \(a(D)\) with symbol \(a(\xi)\) in the class \(S^0 (\mathbb{R}^n)\). It is known that \(a(D)\) is bounded from \(L^p (\mathbb{R}^n)\) to \(L^p (\mathbb{R}^n)\) for \(1<p <\infty\); the author computes in such a frame the spetrum and the essential spectrum of \(a(D)\). An application is given concerning the asymptotic stability of the zero solution of a related semilinear equation.
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 47G30
zbMATH DE Number: 1132994
zbMATH Keywords: spectral properties
zbMATH Keywords: pseudodifferential operator
zbMATH Keywords: spetrum
zbMATH Keywords: essential spectrum
author: M. W. Wong
reviewed by: Luigi Rodino
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1132994