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    • University of Missouri-Columbia
    • Graduate School - MU Theses and Dissertations (MU)
    • Theses and Dissertations (MU)
    • Dissertations (MU)
    • 2006 Dissertations (MU)
    • 2006 MU dissertations - Freely available online
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    Topics in functional analysis and convex geometry

    Yaskina, Maryna, 1979-
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    [PDF] research.pdf (413.2Kb)
    Date
    2006
    Format
    Thesis
    Metadata
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    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 L[0], give a characterization of subspaces of L[0] and confirm the place of L[0] 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.
    URI
    https://hdl.handle.net/10355/4346
    https://doi.org/10.32469/10355/4346
    Degree
    Ph. D.
    Thesis Department
    Mathematics (MU)
    Rights
    OpenAccess.
    Collections
    • 2006 MU dissertations - Freely available online
    • Mathematics electronic theses and dissertations (MU)

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