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Now showing items 1-20 of 153

#### The poisson problem on Lipschitz domains

(University of Missouri--Columbia, 2005)

The aim of this work is to describe the sharp ranges of indices, for which the Poisson problem for Laplacian with Dirichlet or Neumann boundary conditions is well-posed on the scales of Besov and Triebel-Lizorkin spaces ...

#### On the spectra of Schrödinger and Jacobi operators with complex-valued quasi-periodic algebro-geometric coefficients

(University of Missouri--Columbia, 2005)

In this thesis we characterize the spectrum of one-dimensional Schrödinger operators. H = -d2/dx2+V in L2(R; dx) with quasi-periodic complex-valued algebro geometric, potentials V (i.e., potentials V which satisfy one ...

#### The absolute functional calculus for sectorial operators

(University of Missouri--Columbia, 2005)

We introduce the absolute functional calculus for sectorial operators. This notion is stronger than the common holomorphic functional calculus. We are able to improve a key theorem related to the maximal regularity problem ...

#### Potential theory and harmonic analysis methods for quasilinear and Hessian equations

(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

(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

(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 ...

#### A class of Gorenstein Artin algebras of embedding dimension four

(University of Missouri--Columbia, 2007)

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Let R be a polynomial ring in n variables and I be a homogeneous ideal in R. Such an ideal I is called Gorenstein if the quotient R/I has a free ...

#### Distributional estimates for multilinear operators

(University of Missouri--Columbia, 2005)

We prove that if a multilinear operator and all its adjoints map L1 x x L1 to L1/m,oo, then the distribution function of the operator applied to characteristic functions of sets of finite measure has exponential decay at ...

#### Erdős distance problem in the hyperbolic half-plane

(University of Missouri--Columbia, 2009)

The Erd̋os distance problem asks for the minimum number of distinct distances determined by large finite point sets in the plane. The aim of this work is to investigate how the classical techniques employed in the study ...

#### Toroidalization of locally toroidal morphisms

(University of Missouri--Columbia, 2008)

Let X and Y be nonsingular varieties over an algebraically closed field [kappa] of characteristic zero. A toroidal structure on X is a simple normal crossing divisor DX on X. Suppose that DX and DY are toroidal structures ...

#### Box approximation and related techniques in spectral theory

(University of Missouri--Columbia, 2008)

This dissertation is concerned with various aspects of the spectral theory of differential and pseudodifferential operators. It consists of two chapters. The first chapter presents a study of a family of spectral shift ...

#### 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 ...

#### Boundary value problems for the Stokes system in arbitrary Lipschitz domains

(University of Missouri--Columbia, 2008)

The goal of this work is to treat the main boundary value problems for the Stokes system, i.e., (i) the Dirichlet problem with Lp-data and nontangential maximal function estimates, (ii) the Neumann problem with Lp-data and ...

#### Algebraic resolution of formal ideals along a valuation

(University of Missouri--Columbia, 2008)

Let X be a possibly singular complete algebraic variety, defined over a field [kappa] of characteristic zero. X is nonsingular at [rho] [element of] X if OX,[rho] is a regular local ring. The problem of resolution of ...

#### Explorations of geometric combinatorics in vector spaces over finite fields

(University of Missouri--Columbia, 2008)

We study how large a set of points needs to be in a vector space over a finite field in order for the points to determine all of a certain type of geometric structure. In addition we show that there are key differences ...

#### The implicit function theorem for Lipschitz functions and applications

(University of Missouri--Columbia, 2008)

The subject matter of this thesis is the classical Implicit Function Theorem and its generalizations. Dictated by practical applications, it is of interest to relax the hypothesis of the standard Implicit Function Theorem ...

#### Surface to surface changes of variables and applications

(University of Missouri--Columbia, 2008)

The present thesis addresses a number of basic problems in relation to integration over surfaces in the Euclidean space, such as how the surface measure and unit normal changes under a smooth diffeomorphism how the integration ...

#### Transference and Szego's theorem for measure preserving representations

(University of Missouri--Columbia, 2007)

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] We prove analogues of the classical Szeg̈o's theorem concerning approximation by polynomials on the unit circle, and Jensen's inequality involving the ...

#### Elliptic curves and their applications in cryptography

(University of Missouri--Columbia, 2009)

In 1985, Koblitz and Miller proposed elliptic curves to be used for public key cryptosystems. This present thesis examines the role of elliptic curves on cryptography and basic problems involving implementation and security ...