Convergence rate estimates for Trotter product approximations of solution operators for non-autonomous Cauchy problems
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2356 | |
dc.contributor.author | Neidhardt, Hagen | |
dc.contributor.author | Stephan, Artur | |
dc.contributor.author | Zagrebnov, Valentin A. | |
dc.date.accessioned | 2017-03-29T23:50:34Z | |
dc.date.available | 2019-06-28T08:05:23Z | |
dc.date.issued | 2016 | |
dc.description.abstract | In the present paper we advocate the Howland-Evans approach to solution of the abstract non-autonomous Cauchy problem (non-ACP) in a separable Banach space X. The main idea is to reformulate this problem as an autonomous Cauchy problem (ACP) in a new Banach space Lp(I;X), p 2 [1;1), consisting of X-valued functions on the time-interval I. The fundamental observation is a one-to-one correspondence between solution operators (propagators) for a non-ACP and the corresponding evolution semigroups for ACP in Lp(I;X). We show that the latter also allows to apply a full power of the operatortheoretical methods to scrutinise the non-ACP including the proof of the Trotter product approximation formulae with operator-norm estimate of the rate of convergence. The paper extends and improves some recent results in this direction in particular for Hilbert spaces. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/2161 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/2302 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | eng |
dc.subject.other | Trotter product formula | eng |
dc.subject.other | convergence rate | eng |
dc.subject.other | approximation | eng |
dc.subject.other | evolution equations | eng |
dc.subject.other | solution operator | eng |
dc.subject.other | extension theory | eng |
dc.subject.other | perturbation theory | eng |
dc.subject.other | operator splitting | eng |
dc.title | Convergence rate estimates for Trotter product approximations of solution operators for non-autonomous Cauchy problems | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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