L^p-tauberian theorems and L^p-rates for energy decay

We prove $L^p$-analogues of the classical tauberian theorem of Ingham and Karamata, and its variations giving rates of decay. These results are applied to derive $L^p$-decay of operator families arising in the study of the decay of energy for damped wave equations and local energy for wave equations...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Journal of functional analysis 2016-02, Vol.270 (3)
Hauptverfasser:	Batty, Charles, Borichev, Alexander, Tomilov, Yuri
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis of PDEs Complex Variables Dynamical Systems Functional Analysis Mathematics
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page
container_issue	3
container_start_page
container_title	Journal of functional analysis
container_volume	270
creator	Batty, Charles Borichev, Alexander Tomilov, Yuri
description	We prove $L^p$-analogues of the classical tauberian theorem of Ingham and Karamata, and its variations giving rates of decay. These results are applied to derive $L^p$-decay of operator families arising in the study of the decay of energy for damped wave equations and local energy for wave equations in exterior domains. By constructing some examples of critical behaviour we show that the $L^p$-rates of decay obtained in this way are best possible under our assumptions.
doi_str_mv	10.1016/j.jfa.2015.12.003
format	Article
fullrecord	<record><control><sourceid>hal</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_01258057v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>oai_HAL_hal_01258057v1</sourcerecordid><originalsourceid>FETCH-LOGICAL-h119t-6d9099fb3387ba16fd2d761a10142f14d09912dc2eb91545475ed29914b4b4723</originalsourceid><addsrcrecordid>eNotjk1Lw0AURQdRMFZ_gLvZupj43puvZFmKWiHgRreGSWfGNLRJmUQh_94U5S4unAOXy9g9Qo6A5rHLu-hyAtQ5Ug4gL1iGUBoBtpCXLAMgEkjSXLObcewAEI3SGdPV50lM7rsJae96PrVhSOE4ctd7flbJTWHkcUg89CF9zdyHnZtv2VV0hzHc_feKfTw_vW-2onp7ed2sK9EilpMwvoSyjI2UhW0cmujJW4NueawoovKLRfI7Ck2JWmlldfC0MNUssSRX7OFvt3WH-pT2R5fmenD7eruu6jMDJF2Atj8ofwEPaUhM</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>L^p-tauberian theorems and L^p-rates for energy decay</title><source>Elsevier ScienceDirect Journals</source><source>EZB-FREE-00999 freely available EZB journals</source><creator>Batty, Charles ; Borichev, Alexander ; Tomilov, Yuri</creator><creatorcontrib>Batty, Charles ; Borichev, Alexander ; Tomilov, Yuri</creatorcontrib><description>We prove $L^p$-analogues of the classical tauberian theorem of Ingham and Karamata, and its variations giving rates of decay. These results are applied to derive $L^p$-decay of operator families arising in the study of the decay of energy for damped wave equations and local energy for wave equations in exterior domains. By constructing some examples of critical behaviour we show that the $L^p$-rates of decay obtained in this way are best possible under our assumptions.</description><identifier>ISSN: 0022-1236</identifier><identifier>EISSN: 1096-0783</identifier><identifier>DOI: 10.1016/j.jfa.2015.12.003</identifier><language>eng</language><publisher>Elsevier</publisher><subject>Analysis of PDEs ; Complex Variables ; Dynamical Systems ; Functional Analysis ; Mathematics</subject><ispartof>Journal of functional analysis, 2016-02, Vol.270 (3)</ispartof><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><orcidid>0000-0003-0068-2964</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,776,780,881,27903,27904</link.rule.ids><backlink>$$Uhttps://hal.science/hal-01258057$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Batty, Charles</creatorcontrib><creatorcontrib>Borichev, Alexander</creatorcontrib><creatorcontrib>Tomilov, Yuri</creatorcontrib><title>L^p-tauberian theorems and L^p-rates for energy decay</title><title>Journal of functional analysis</title><description>We prove $L^p$-analogues of the classical tauberian theorem of Ingham and Karamata, and its variations giving rates of decay. These results are applied to derive $L^p$-decay of operator families arising in the study of the decay of energy for damped wave equations and local energy for wave equations in exterior domains. By constructing some examples of critical behaviour we show that the $L^p$-rates of decay obtained in this way are best possible under our assumptions.</description><subject>Analysis of PDEs</subject><subject>Complex Variables</subject><subject>Dynamical Systems</subject><subject>Functional Analysis</subject><subject>Mathematics</subject><issn>0022-1236</issn><issn>1096-0783</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNotjk1Lw0AURQdRMFZ_gLvZupj43puvZFmKWiHgRreGSWfGNLRJmUQh_94U5S4unAOXy9g9Qo6A5rHLu-hyAtQ5Ug4gL1iGUBoBtpCXLAMgEkjSXLObcewAEI3SGdPV50lM7rsJae96PrVhSOE4ctd7flbJTWHkcUg89CF9zdyHnZtv2VV0hzHc_feKfTw_vW-2onp7ed2sK9EilpMwvoSyjI2UhW0cmujJW4NueawoovKLRfI7Ck2JWmlldfC0MNUssSRX7OFvt3WH-pT2R5fmenD7eruu6jMDJF2Atj8ofwEPaUhM</recordid><startdate>201602</startdate><enddate>201602</enddate><creator>Batty, Charles</creator><creator>Borichev, Alexander</creator><creator>Tomilov, Yuri</creator><general>Elsevier</general><scope>1XC</scope><orcidid>https://orcid.org/0000-0003-0068-2964</orcidid></search><sort><creationdate>201602</creationdate><title>L^p-tauberian theorems and L^p-rates for energy decay</title><author>Batty, Charles ; Borichev, Alexander ; Tomilov, Yuri</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-h119t-6d9099fb3387ba16fd2d761a10142f14d09912dc2eb91545475ed29914b4b4723</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Analysis of PDEs</topic><topic>Complex Variables</topic><topic>Dynamical Systems</topic><topic>Functional Analysis</topic><topic>Mathematics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Batty, Charles</creatorcontrib><creatorcontrib>Borichev, Alexander</creatorcontrib><creatorcontrib>Tomilov, Yuri</creatorcontrib><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Journal of functional analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Batty, Charles</au><au>Borichev, Alexander</au><au>Tomilov, Yuri</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>L^p-tauberian theorems and L^p-rates for energy decay</atitle><jtitle>Journal of functional analysis</jtitle><date>2016-02</date><risdate>2016</risdate><volume>270</volume><issue>3</issue><issn>0022-1236</issn><eissn>1096-0783</eissn><abstract>We prove $L^p$-analogues of the classical tauberian theorem of Ingham and Karamata, and its variations giving rates of decay. These results are applied to derive $L^p$-decay of operator families arising in the study of the decay of energy for damped wave equations and local energy for wave equations in exterior domains. By constructing some examples of critical behaviour we show that the $L^p$-rates of decay obtained in this way are best possible under our assumptions.</abstract><pub>Elsevier</pub><doi>10.1016/j.jfa.2015.12.003</doi><orcidid>https://orcid.org/0000-0003-0068-2964</orcidid></addata></record>
fulltext	fulltext
identifier	ISSN: 0022-1236
ispartof	Journal of functional analysis, 2016-02, Vol.270 (3)
issn	0022-1236 1096-0783
language	eng
recordid	cdi_hal_primary_oai_HAL_hal_01258057v1
source	Elsevier ScienceDirect Journals; EZB-FREE-00999 freely available EZB journals
subjects	Analysis of PDEs Complex Variables Dynamical Systems Functional Analysis Mathematics
title	L^p-tauberian theorems and L^p-rates for energy decay
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-27T16%3A36%3A26IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-hal&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=L%5Ep-tauberian%20theorems%20and%20L%5Ep-rates%20for%20energy%20decay&rft.jtitle=Journal%20of%20functional%20analysis&rft.au=Batty,%20Charles&rft.date=2016-02&rft.volume=270&rft.issue=3&rft.issn=0022-1236&rft.eissn=1096-0783&rft_id=info:doi/10.1016/j.jfa.2015.12.003&rft_dat=%3Chal%3Eoai_HAL_hal_01258057v1%3C/hal%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true