• 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 ...
  • Complex and almost-complex structures on six dimensional manifolds 

    Brown, James Ryan, 1977- (University of Missouri--Columbia, 2006)
    We investigate the properties of hypothetical exotic complex structures on three dimensional complex projective space CP³. This is motivated by the long standing question in differential geometry of whether or not the six ...
  • Directional time-frequency analysis with applications 

    Sansing, Christopher, 1979- (University of Missouri--Columbia, 2006)
    The purpose of this dissertation is to introduce a new directionally-sensitive time frequency representation of a function. It is shown that we may break up a function (or signal) into individual time-frequency-direction ...
  • Parabolic layer potentials and initial boundary value problems in Lipschitz cylinders with data in Besov spaces 

    Jakab, Tunde, 1974- (University of Missouri--Columbia, 2006)
    We adapt the method of boundary layer potentials to the Poisson problem for the heat operator [partial differential]t [delta] in a bounded Lipschitz cylinder, with Dirichlet and Neumann boundary conditions. When the lateral ...
  • Potential theory and harmonic analysis methods for quasilinear and Hessian equations 

    Nguyen, Phuc Cong, 1976- (University of Missouri--Columbia, 2006)
    The existence problem is solved, and global pointwise estimates of solutions are obtained for quasilinear and Hessian equations of Lane-Emden type, including the following two model problems:-[delta]pu = uq + [mu], Fk[-u] ...
  • Sharp estimates of the transmission boundary value problem for dirac operators on non-smooth domains 

    Shi, Qiang, 1976- (University of Missouri--Columbia, 2006)
    This thesis derives the sharp estimates for the transmission boundary value problems (TBVP) for Dirac operators in Lipschitz domains in the three dimensional setting. Most of the transmission problems considered in the ...
  • 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 ...
  • Topics in spectral and inverse spectral theory 

    Zinchenko, Maksym, 1980- (University of Missouri--Columbia, 2006)
    This dissertation is concerned with two major classes of operators and provides various spectral and inverse spectral results for them. In the first part of this work a special class of one-dimensional discrete unitary ...