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dc.contributor.advisorAsmar, Nakhlé H.eng
dc.contributor.authorKoucherik, Elena, 1962-eng
dc.date.issued2007eng
dc.date.submitted2007 Falleng
dc.descriptionThe entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.eng
dc.descriptionTitle from title screen of research.pdf file (viewed on March 11, 2008)eng
dc.descriptionThesis (Ph. D.) University of Missouri-Columbia 2007.eng
dc.description.abstract[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] We prove analogues of the classical Szeg̈o's theorem concerning approximation by polynomials on the unit circle, and Jensen's inequality involving the summability of the logarithm, for functions in generalized Hardy spaces Hp([gamma],[mu]). The latter are defined in terms of strongly continuous, measure preserving representations in Lp([gamma],[mu]), where ([gamma],[mu]) is a locally compact measure space. In a similar framework, Asmar and Montgomery-Smith earlier obtained an analogue of the F. and M. Riesz theorem, which generalizes deep results due to de Leeuw and Glicksberg, and Forelli. Our approach employs a variety of methods, including elements of transference theory, representation theory, operator theory, and spectral theory of functions. We develop the notions of convolutions, spectra, analytic decompositions, generalized trigonometric and analytic trigonometric polynomials on ([gamma],[mu]), and study their approximation properties. This enables us to obtain broad generalizations of some results of the classical theory, which corresponds to the special case where measure preserving representations are generated by translations on the unit circle.eng
dc.description.bibrefIncludes bibliographical referenceseng
dc.identifier.merlinb62634677eng
dc.identifier.oclc213339499eng
dc.identifier.urihttps://doi.org/10.32469/10355/6018eng
dc.identifier.urihttps://hdl.handle.net/10355/6018
dc.languageEnglisheng
dc.publisherUniversity of Missouri--Columbiaeng
dc.relation.ispartofcommunityUniversity of Missouri--Columbia. Graduate School. Theses and Dissertationseng
dc.rightsAccess is limited to the campuses of the University of Missouri.eng
dc.subject.lcshApproximation theoryeng
dc.subject.lcshLogarithmseng
dc.subject.lcshOperator theoryeng
dc.subject.lcshSpectral theory (Mathematics)eng
dc.titleTransference and Szego's theorem for measure preserving representationseng
dc.typeThesiseng
thesis.degree.disciplineMathematics (MU)eng
thesis.degree.grantorUniversity of Missouri--Columbiaeng
thesis.degree.levelDoctoraleng
thesis.degree.namePh. D.eng


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