Linear evolution equations with strongly measurable families and application to the Dirac equation
type: Item
instance of: scholarly article
title: Linear evolution equations with strongly measurable families and application to the Dirac equation
zbMATH Open document ID: 1236.47040
author: Noboru Okazawa
author: Kentarou Yoshii
published in: Discrete and Continuous Dynamical Systems. Series S
publication date: 2011-03-22T00:00:00Z
review text: Let \(\{A(t)\}\) be a family of closed linear operators in a separable Hilbert space \(X\), and \(S\) a selfadjoint operator in \(X\) satisfying \[ (u, Su)\geq \|u\|^2 \quad \text{for all } u\in D(S). \] Under some conditions associated with \(\{A(t)\}\) and \(S\), the authors, by a modified Yosida approximation, construct a two-parameter family \(\{U(t,s): 0\leq s\leq t\leq T\}\) satisfying certain properties. Applications to the Dirac equation are given.
reviewed by: Jin Liang
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47B44
Mathematics Subject Classification ID: 35L45
zbMATH DE Number: 5869377
zbMATH Keywords: evolution operator
zbMATH Keywords: selfadjoint operator
zbMATH Keywords: separable Hilbert space
zbMATH Keywords: Dirac equation
zbMATH Keywords: hyperbolic type
zbMATH Keywords: measurable coefficients
MaRDI profile type: Publication
full work available at URL: dcdss.2011.4.723
OpenAlex ID: W2328157332
DOI: 10.3934/DCDSS.2011.4.723
description: scientific article; zbMATH DE number 5869377