Browsing Department of Mathematics (MU) by Thesis Advisor "Koldobsky, Alexander, 1955"
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Applications of fourier analysis to intersection bodies
(University of MissouriColumbia, 2008)The concept of an intersection body is central for the dual BrunnMinkowski theory and has played an important role in the solution of the BusemannPetty problem. A more general concept of [kappa]intersection bodies is ... 
Applications of the fourier transform to convex geometry
(University of MissouriColumbia, 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 BusemannPetty problem and ... 
Geometric and nonlinear limit theorems in probability theory
(University of MissouriColumbia, 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
(University of MissouriColumbia, 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
(University of MissouriColumbia, 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 nonintersection body all of whose ... 
Uniqueness theorems for nonsymmetric convex bodies
(University of MissouriColumbia, 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 ...