Topics in functional analysis and convex geometry

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Topics in functional analysis and convex geometry

Please use this identifier to cite or link to this item: http://hdl.handle.net/10355/4346

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dc.contributor.advisor Koldobsky, Alexander, 1955- en
dc.contributor.author Yaskina, Maryna, 1979- en_US
dc.date.accessioned 2010-01-12T17:05:27Z
dc.date.available 2010-01-12T17:05:27Z
dc.date.issued 2006 en_US
dc.date.submitted 2006 Spring en
dc.identifier.other YaskinaM-042106-D4583 en_US
dc.identifier.uri http://hdl.handle.net/10355/4346
dc.description The 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.description Title from title screen of research.pdf file viewed on (March 1, 2007) en_US
dc.description Includes bibliographical references. en_US
dc.description Vita. en_US
dc.description Thesis (Ph.D.) University of Missouri-Columbia 2006. en_US
dc.description Dissertations, Academic -- University of Missouri--Columbia -- Mathematics. en_US
dc.description.abstract In 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.language.iso en_US en_US
dc.publisher University of Missouri--Columbia en_US
dc.relation.ispartof 2006 Freely available dissertations (MU) en_US
dc.subject.lcsh Convex geometry en_US
dc.subject.lcsh Fourier transformations en_US
dc.subject.lcsh Geometric function theory en_US
dc.title Topics in functional analysis and convex geometry en_US
dc.type Thesis en_US
thesis.degree.discipline Mathematics en_US
thesis.degree.grantor University of Missouri--Columbia en_US
thesis.degree.name Ph.D. en_US
thesis.degree.level Doctoral en_US
dc.identifier.merlin .b57908576 en_US
dc.identifier.oclc 85484656 en_US
dc.relation.ispartofcommunity University of Missouri-Columbia. Graduate School. Theses and Dissertations. Dissertations. 2006 Dissertations


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