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Applications of fourier analysis to intersection bodies
(University of Missouri--Columbia, 2008)
of the Busemann-Petty problem. We are interested in comparing classes of [kappa]-intersection bodies. In the first chapter we present the result that was published in J. Schlieper, A note on [kappa]-intersection bodies, Proceedings American. Mathematical Society...
Some results in convex geometry
(University of Missouri--Columbia, 2016)
This thesis is divided into four parts. The first part is about proving that the unit ball of the Lorentz space is not an intersection body for dimension greater than or equal to 5 and q > 2. We go on to explain the ...
Geometric and nonlinear limit theorems in probability theory
(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 ...
Uniqueness theorems for non-symmetric convex bodies
(University of Missouri--Columbia, 2009)
determined by the Gaussian covariogram. The Gaussian covariogram of a body K is a function that yields the standard Gaussian measure of the intersection of K with its translates.--From public.pdf....
Topics in functional analysis and convex geometry
(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 ...
Sections of complex convex bodies
(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 ...
Applications of the fourier transform to convex geometry
(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 ...