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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 ...
Uniqueness theorems for non-symmetric convex bodies
(University of Missouri--Columbia, 2009)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] This dissertation involves the determination of convex bodies and the comparison of sections of convex bodies. Uniqueness of convex bodies via derivatives ...
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 fourier analysis to intersection bodies
(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 ...
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 ...
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 ...
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 ...