Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.4176
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dc.contributor.authorSeifert, Christian-
dc.contributor.authorTrostorff, Sascha-
dc.contributor.authorWaurick, Marcus-
dc.date.accessioned2022-02-24T08:13:57Z-
dc.date.available2022-02-24T08:13:57Z-
dc.date.issued2021-09-28-
dc.identifier.citationOperator Theory: Advances and Applications 287: 119-130 (2022-01-01)de_DE
dc.identifier.isbn978-3-030-89397-2de_DE
dc.identifier.isbn978-3-030-89396-5de_DE
dc.identifier.urihttp://hdl.handle.net/11420/11750-
dc.description.abstractIn this chapter we turn our focus back to causal operators. In Chap. 5 we found out that material laws provide a class of causal and autonomous bounded operators. In this chapter we will present another proof of this fact, which rests on a result which characterises functions in L2(ℝ; H) with support contained in the non-negative reals; the celebrated Theorem of Paley and Wiener. With the help of this theorem, which is interesting in its own right, the proof of causality for material laws becomes very easy. At a first glance it seems that holomorphy of a material law is a rather strong assumption. In the second part of this chapter, however, we shall see that in designing autonomous and causal solution operators, there is no way of circumventing holomorphy.en
dc.language.isoende_DE
dc.publisherSpringerde_DE
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/de_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleCausality and a Theorem of paley and wienerde_DE
dc.typeinBookde_DE
dc.identifier.doi10.15480/882.4176-
dc.type.dinibookPart-
dcterms.DCMITypeText-
tuhh.identifier.urnurn:nbn:de:gbv:830-882.0173067-
tuhh.oai.showtruede_DE
tuhh.abstract.englishIn this chapter we turn our focus back to causal operators. In Chap. 5 we found out that material laws provide a class of causal and autonomous bounded operators. In this chapter we will present another proof of this fact, which rests on a result which characterises functions in L2(ℝ; H) with support contained in the non-negative reals; the celebrated Theorem of Paley and Wiener. With the help of this theorem, which is interesting in its own right, the proof of causality for material laws becomes very easy. At a first glance it seems that holomorphy of a material law is a rather strong assumption. In the second part of this chapter, however, we shall see that in designing autonomous and causal solution operators, there is no way of circumventing holomorphy.de_DE
tuhh.publisher.doi10.1007/978-3-030-89397-2_8-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.identifier.doi10.15480/882.4176-
tuhh.type.opusInBuch (Kapitel / Teil einer Monographie)-
dc.type.driverbookPart-
dc.type.casraiBook Chapter-
tuhh.container.startpage119de_DE
tuhh.container.endpage130de_DE
dc.rights.nationallicensefalsede_DE
tuhh.relation.ispartofseriesOperator theoryde_DE
tuhh.relation.ispartofseriesnumber287de_DE
dc.identifier.scopus2-s2.0-85124413059de_DE
local.status.inpressfalsede_DE
local.type.versionpublishedVersionde_DE
datacite.resourceTypeBook Chapter-
datacite.resourceTypeGeneralText-
item.languageiso639-1en-
item.grantfulltextopen-
item.creatorOrcidSeifert, Christian-
item.creatorOrcidTrostorff, Sascha-
item.creatorOrcidWaurick, Marcus-
item.mappedtypeinBook-
item.tuhhseriesidOperator theory-
item.creatorGNDSeifert, Christian-
item.creatorGNDTrostorff, Sascha-
item.creatorGNDWaurick, Marcus-
item.seriesrefOperator theory;287-
item.fulltextWith Fulltext-
item.openairetypeinBook-
item.openairecristypehttp://purl.org/coar/resource_type/c_3248-
item.cerifentitytypePublications-
crisitem.author.deptMathematik E-10-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0001-9182-8687-
crisitem.author.orcid0000-0003-4498-3574-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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