Browsing 2006 MU dissertations  Freely available online by Thesis Department "Mathematics"
Now showing items 18 of 8

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 ... 
Complex and almostcomplex structures on six dimensional manifolds
(University of MissouriColumbia, 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 timefrequency analysis with applications
(University of MissouriColumbia, 2006)The purpose of this dissertation is to introduce a new directionallysensitive time frequency representation of a function. It is shown that we may break up a function (or signal) into individual timefrequencydirection ... 
Parabolic layer potentials and initial boundary value problems in Lipschitz cylinders with data in Besov spaces
(University of MissouriColumbia, 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
(University of MissouriColumbia, 2006)The existence problem is solved, and global pointwise estimates of solutions are obtained for quasilinear and Hessian equations of LaneEmden 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 nonsmooth domains
(University of MissouriColumbia, 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
(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 ... 
Topics in spectral and inverse spectral theory
(University of MissouriColumbia, 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 onedimensional discrete unitary ...