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dc.contributor.advisorKoldobsky, Alexander, 1955-en
dc.contributor.authorYaskina, Maryna, 1979-en_US
dc.date.issued2006eng
dc.date.submitted2006 Springen
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.en_US
dc.descriptionTitle from title screen of research.pdf file viewed on (March 1, 2007)en_US
dc.descriptionIncludes bibliographical references.en_US
dc.descriptionVita.en_US
dc.descriptionThesis (Ph.D.) University of Missouri-Columbia 2006.en_US
dc.descriptionDissertations, Academic -- University of Missouri--Columbia -- Mathematics.en_US
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.en_US
dc.identifier.merlin.b57908576en_US
dc.identifier.oclc85484656en_US
dc.identifier.otherYaskinaM-042106-D4583en_US
dc.identifier.urihttp://hdl.handle.net/10355/4346
dc.publisherUniversity of Missouri--Columbiaen_US
dc.relation.ispartof2006 Freely available dissertations (MU)en_US
dc.relation.ispartofcommunityUniversity of Missouri-Columbia. Graduate School. Theses and Dissertations. Dissertations. 2006 Dissertations
dc.subject.lcshConvex geometryen_US
dc.subject.lcshFourier transformationsen_US
dc.subject.lcshGeometric function theoryen_US
dc.titleTopics in functional analysis and convex geometryen_US
dc.typeThesisen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.disciplineMathematicseng
thesis.degree.grantorUniversity of Missouri--Columbiaen_US
thesis.degree.levelDoctoralen_US
thesis.degree.namePh.D.en_US


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