Regularized quasi-spectral distributions
type: Item
instance of: scholarly article
title: Regularized quasi-spectral distributions
zbMATH Open document ID: 0909.47030
DOI: 10.1023/A:1006534907063
author: Sheng Wang Wang
author: R. deLaubenfels
published in: Acta Mathematica Hungarica
publication date: 1998-11-24T00:00:00Z
review text: The authors deal with a generalization of a spectral distribution, that they call a quasi-spectral distribution, that removes any density condition from the definition of a spectral distribution; in particular, the momentum needs not be densely defined, but a \(C^\infty({\mathbb{R}})\) functional calculus is constructed for it. Relations between regularized quasi-spectral distributions and \(C^\infty\) functional calculi as well as the relationship between the momentum of a certain class of \(C\)-regularized quasi-spectral distributions, and the generator of a generalization of strongly continuous groups, \(C\)-regularized groups and locally Lipschitz-continuous once-integrated \(C\)-regularized groups are considered. A generalization of Stone's theorem characterizes the momenta of certain (regularized) quasi-spectral distributions as generators of polynomially bounded once-integrated (regularized) groups.
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 46H30
Mathematics Subject Classification ID: 46F99
zbMATH DE Number: 1226459
zbMATH Keywords: quasi-spectral distributions
zbMATH Keywords: functional calculus
zbMATH Keywords: \(C\)-regularized groups
zbMATH Keywords: Lipschitz-continuous once-integrated \(C\)-regularized groups
reviewed by: Petre P. Teodorescu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1226459