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dc.contributor.advisorKoldobsky, Alexander, 1955-eng
dc.contributor.authorYaskina, Maryna, 1979-eng
dc.date.issued2006eng
dc.date.submitted2006 Springeng
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 1, 2007)eng
dc.descriptionIncludes bibliographical references.eng
dc.descriptionVita.eng
dc.descriptionThesis (Ph.D.) University of Missouri-Columbia 2006.eng
dc.descriptionDissertations, Academic -- University of Missouri--Columbia -- Mathematics.eng
dc.description.abstractIn this thesis we study different problems in Convex Geometry with the aid of the Fourier Transform and tools of Functional Analysis. In the second chapter we construct an example of a non-intersection body all of whose central sections are intersection bodies. The third chapter is devoted to the study of the geometry of L0. We introduce the definition of embedding of a normed space in L₀, give a characterization of subspaces of L₀ and confirm the place of L₀ in the scale of L[subscript p] spaces. In the fourth chapter we modify the assumptions of the original Busemann-Petty problem in order to obtain the positive answer in all dimensions. Chapter five is focused on L [subscript p]-centroid bodies and generalization of some results of Lutwak and Grinberg, Zhang to [minus] 1 [less than] p [less than] 1.eng
dc.identifier.merlin.b57908576eng
dc.identifier.oclc85484656eng
dc.identifier.otherYaskinaM-042106-D4583eng
dc.identifier.urihttp://hdl.handle.net/10355/4346eng
dc.languageEnglisheng
dc.publisherUniversity of Missouri--Columbiaeng
dc.relation.ispartofcollectionUniversity of Missouri-Columbia. Graduate School. Theses and Dissertations.eng
dc.subject.lcshConvex geometryeng
dc.subject.lcshFourier transformationseng
dc.subject.lcshGeometric function theoryeng
dc.titleTopics in functional analysis and convex geometryeng
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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