Generalized asymptotic constants
type: Item
instance of: scholarly article
title: Generalized asymptotic constants
zbMATH Open document ID: 0656.47002
DOI: 10.1007/BF01057289
published in: Ukrainian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: Let \(U_ t=\exp (-iHt)\) be an evolution in the Hilbert space \({\mathcal H}\). A bounded operator X in \({\mathcal H}\) is said to be a smooth asymptotic constant if on some set of vectors in \({\mathcal H}\quad \quad U_{-t}XU_ t\) converges very rapidly as \(t\to \infty\) [see, for details, \textit{M. Wollenberg}, Math. Nachr. 126, 217-229 (1986; Zbl 0609.47017)]. In some applications (e.g. scattering theory) interesting cases appear in which X is not bounded. In the paper under review an abstract notion of generalised asymptotic constant (X unbounded) is introduced and some of its elementary properties are investigated.
Mathematics Subject Classification ID: 47A40
zbMATH DE Number: 4071698
zbMATH Keywords: wave operator
zbMATH Keywords: evolution
zbMATH Keywords: Hilbert space
zbMATH Keywords: scattering theory
zbMATH Keywords: generalised asymptotic constant
author: Manfred Wollenberg
author: Volodymyr Koshmanenko
reviewed by: Gheorghe Nenciu
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01057289
OpenAlex ID: W2052390942
description: scientific article; zbMATH DE number 4071698