• Applications of fourier analysis to intersection bodies 

    Schlieper, Jared (University of Missouri--Columbia, 2008)
    The concept of an intersection body is central for the dual Brunn-Minkowski theory and has played an important role in the solution of the Busemann-Petty problem. A more general concept of [kappa]-intersection bodies is ...
  • Applications of the fourier transform to convex geometry 

    Yaskin, Vladyslav, 1974- (University of Missouri--Columbia, 2006)
    The thesis is devoted to the study of various problems arising from Convex Geometry and Geometric Functional Analysis using tools of Fourier Analysis. In chapters two through four we consider the Busemann-Petty problem and ...
  • Geometric and nonlinear limit theorems in probability theory 

    Fresen, Daniel John (University of Missouri--Columbia, 2012)
    The concentration of measure phenomenon is a nonlinear equivalent of the law of large numbers that deals with real valued Lipschitz functions and includes linear functionals such as the sample mean. In the first part of ...
  • Sections of complex convex bodies 

    Zymonopoulou, Maria-Isavella, 1973- (University of Missouri--Columbia, 2008)
    The main idea of the Fourier analytic approach to sections of convex bodies is to express different parameters of a body in terms of the Fourier transform and then apply methods of Fourier analysis to solve geometric ...
  • Topics in functional analysis and convex geometry 

    Yaskina, Maryna, 1979- (University of Missouri--Columbia, 2006)
    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 ...
  • Uniqueness theorems for non-symmetric convex bodies 

    Shane, Christopher, 1978- (University of Missouri--Columbia, 2009)
    The first uniqueness result involves fractional derivatives of parallel section functions. It is proven that if [negative]1 [lesser than] q [lesser than] n [negative]1 is not an integer, then the ...