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Stability theory for semigroups using (Lp,Lq) Fourier multipliers

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Rozendaal, Jan; Veraar, Mark

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We study polynomial and exponential stability for C0-semigroups using the recently developed theory of operator-valued (Lp,Lq) Fourier multipliers. We characterize polynomial decay of orbits of a C0-semigroup in terms of the (Lp,Lq) Fourier multiplier properties of its resolvent. Using this characterization we derive new polynomial decay rates which depend on the geometry of the underlying space. We do not assume that the semigroup is uniformly bounded, our results depend only on spectral...[Show more]

dc.contributor.authorRozendaal, Jan
dc.contributor.authorVeraar, Mark
dc.date.accessioned2020-04-23T10:52:15Z
dc.identifier.issn0022-1236
dc.identifier.urihttp://hdl.handle.net/1885/203396
dc.description.abstractWe study polynomial and exponential stability for C0-semigroups using the recently developed theory of operator-valued (Lp,Lq) Fourier multipliers. We characterize polynomial decay of orbits of a C0-semigroup in terms of the (Lp,Lq) Fourier multiplier properties of its resolvent. Using this characterization we derive new polynomial decay rates which depend on the geometry of the underlying space. We do not assume that the semigroup is uniformly bounded, our results depend only on spectral properties of the generator. As a corollary of our work on polynomial stability we reprove and unify various existing results on exponential stability, and we also obtain a new theorem on exponential stability for positive semigroups.
dc.description.sponsorshipThe first author is partially supported by grant DP160100941 of the Australian Research Council. The second author is supported by the VIDI subsidy 639.032.427 of the Netherlands Organisation for Scientific Research (NWO).
dc.format.mimetypeapplication/pdf
dc.language.isoen_AU
dc.publisherAcademic Press
dc.rights© 2018 Elsevier Inc
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.sourceJournal of Functional Analysis
dc.subjectC0-semigroup Polynomial and exponential stability Fourier multipliers Type and cotype
dc.titleStability theory for semigroups using (Lp,Lq) Fourier multipliers
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume275
dc.date.issued2018
local.identifier.absfor010108 - Operator Algebras and Functional Analysis
local.identifier.ariespublicationu5013521xPUB31
local.publisher.urlhttps://www.elsevier.com/en-au
local.type.statusAccepted Version
local.contributor.affiliationRozendaal, Jan, College of Science, ANU
local.contributor.affiliationVeraar, Mark, Delft University of Technology
dc.relationhttp://purl.org/au-research/grants/arc/DP160100941
local.bibliographicCitation.issue10
local.bibliographicCitation.startpage2845
local.bibliographicCitation.lastpage2894
local.identifier.doi10.1016/j.jfa.2018.06.015
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
dc.date.updated2019-11-25T07:57:31Z
local.identifier.scopusID2-s2.0-85049331672
local.identifier.thomsonID000445320100008
dcterms.accessRightsOpen Access
dc.rights.licenseCreative Commons Attribution Non-Commercial No Derivatives License
CollectionsANU Research Publications

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