A measure disintegration approach to spectral multiplicity for normal operators

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buir.advisorGheondea, Aurelian
dc.contributor.authorAy, Serdar
dc.date.accessioned2016-01-08T18:23:32Z
dc.date.available2016-01-08T18:23:32Z
dc.date.issued2012
dc.departmentDepartment of Mathematicsen_US
dc.descriptionAnkara : The Department of Mathematics and the Graduate School of Engineering and Science of Bilkent University, 2012.en_US
dc.descriptionThesis (Master's) -- Bilkent University, 2012.en_US
dc.descriptionIncludes bibliographical references leaves 44-45.en_US
dc.description.abstractIn this thesis we studied the notion of direct integral Hilbert spaces, first introduced by J. von Neumann, and the closely related notion of decomposable operators, as defined in Kadison and Ringrose [1997] and Abrahamse and Kriete [1973]. Examples which show that some of the most familiar spaces in analysis are direct integral Hilbert spaces are presented in detail. Then we give a careful treatment of the notion of disintegration of a probability measure on a locally compact separable metric space, and using the machinery we obtain, a proof of the Spectral Multiplicity Theorem for Normal Operators employing the notion of disintegration of measures is given, based on Abrahamse and Kriete [1973], Arveson [1976], Arveson [2002]. In Chapter 5 the notion of essential preimage is presented in the sense of the article Abrahamse and Kriete [1973], and its relation with the spectral multiplicity function is discussed.en_US
dc.description.degreeM.S.en_US
dc.description.statementofresponsibilityAy, Serdaren_US
dc.format.extentvi, 45 leaves, 30 cmen_US
dc.identifier.urihttp://hdl.handle.net/11693/15711
dc.language.isoEnglishen_US
dc.publisherBilkent Universityen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectdirect integral Hilbert spaceen_US
dc.subjectdisintegration of measuresen_US
dc.subjectnormal operatorsen_US
dc.subjectSpectral Multiplicity Theoremen_US
dc.subjectmultiplicity functionen_US
dc.subject.lccQA320 .A9 2012en_US
dc.subject.lcshSpectral theory (Mathematics)en_US
dc.subject.lcshHilbert space.en_US
dc.subject.lcshFunctional analysis.en_US
dc.subject.lcshOperator theory.en_US
dc.subject.lcshMeasure theory.en_US
dc.titleA measure disintegration approach to spectral multiplicity for normal operatorsen_US
dc.typeThesisen_US

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