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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 ...
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 ...
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 ...
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 ...
Trace formulae in finite von Neumann algebras
(University of Missouri--Columbia, 2007)
The dissertation is devoted to some aspects of spectral perturbation theory in the context of finite Von Neumann algebras. The central results are analogs of the Birman-Schwinger principle and the Birman-Krein formula for ...
Volatility estimation and price prediction using a hidden Markov model with empirical study
(University of Missouri--Columbia, 2007)
This work provides a solid development of a hidden Markov model (HMM) from the economic insight to the mathematic formulation. In this model, we assume both drift and volatility of the security return process are driven ...
Parabolic layer potentials and initial boundary value problems in Lipschitz cylinders with data in Besov spaces
(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 ...
Topics in spectral and inverse spectral theory
(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 ...
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 ...
Complex and almost-complex structures on six dimensional manifolds
(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
(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 ...
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 ...
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 ...
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 ...
Incorporation of directionally dependent diffusion with polymer composite flow theory
(University of Missouri--Columbia, 2006)
The extensive industrial use of short-fiber reinforced polymer composites demands an accurate understanding of fiber orientation kinematics. There is a growing concern in recent literature with the popular Folgar and Tucker ...
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 ...
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 ...
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 ...