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Topics in geometric analysis with applications to partial differential equations
(University of Missouri--Columbia, 2009)
The main aim of the current thesis is to investigate the mathematical tools and methods used to study problems which bridge between analysis and geometry. Such an undertaking is particularly useful in situations in which ...
Topics in non-locally convex functional analysis and geometrical analysis with applications to boundary value problems
(University of Missouri--Columbia, 2012)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] This dissertation is comprised of two parts. The first part, consisting of chapters 2-13, deals with issues pertaining to non-locally functional analysis. ...
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 ...
Foundations of geometry
(University of Missouri--Columbia, 1901)
Geometry has been called the science of in-direct measurement, and as such is founded on certain definitions, postulates, and some assumptions or axioms which are said to be self-evident. It is a physical science idealized. ...
Singular solutions of differential equations of the first order
(University of Missouri--Columbia, 1900)
A differential equation may be formed from all algebraic equations by the elimination of the arbitrary constants between the latter and its derivatives. The number of derivations being equal to the number of arbitrary ...
Generalized local Tb theorem and applications
(University of Missouri--Columbia, 2012)
The Tb theorem, like its predecessor, the T1 Theorem, is an L2 boundedness criterion, originally established by McIntosh and Meyer, and by David, Journé and Semmes in the context of singular integrals, but later extended ...
Conditionally convergent vector series
(University of Missouri--Columbia, 1914)
In this paper we propose to study the behavior of series of complex numbers, or of vectors in two dimensions; and to generalize this study to the case of vectors in n dimensions. The particular properties to be studied are ...
A collection of graphs to accompany certain topics in the study of function theory of a real variable
(University of Missouri--Columbia, 1913)
In Part I of this paper, I have dealt with only well-known properties of functions - treating them from the graphic standpoint entirely and referring the reader, to the best authorities I could find, for the Algebraic ...
Oscillation of certain sets of orthogonal functions
(University of Missouri--Columbia, 1914)
In the classic memoirs of Sturm and Liouville, two classes of theorems are found concerning sets of orthogonal functions. The first deal with the number of sign-changes in [phi]3, and the second with the number of sign-changes ...
Study of the convergence of series in certain orthogonal functions
(University of Missouri--Columbia, 1914)
In this present paper we will develop some theorems concerning the degree of convergence of certain series, in particular a Fourier's series, a Legendre's series, and a series of Bessel's functions. Before proceeding ...
Some new aspects of the Galois theory
(University of Missouri--Columbia, 1913)
Realizing that the Galois theory of algebraic equations as commonly presented seems artificial, abstract, and intricate, we have been led in the following paper to attempt to present in a clear, tangible fashion the general, ...
The Evans function, the Weyl-Titchmarsh function, and the Birman-Schwinger operators
(University of Missouri--Columbia, 2012)
We focus on the spectral stability of travelling wave solutions of partial differential equations. First, we use the Gohberg-Rouche Theorem to prove equality of the algebraic multiplicity of an isolated eigenvalue of an ...
Topics in Littlewood-Paley theory and BMO
(University of Missouri--Columbia, 2012)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] In this thesis we discuss some important results in Littlewood-Paley theory and the space of Bounded-Mean Oscillation functions, henceforth called ...
Complemented block bases of symmetric bases and spectral tetris fusion frame constructions
(University of Missouri--Columbia, 2012)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] This work contains of two parts which are totally unrelated. In the first part we consider techniques surrounding the problem whether a complemented ...
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 ...
Existence and construction of real-valued equiangular tight frames
(University of Missouri--Columbia, 2009)
This paper presents results on real-valued equiangular tight frames (ETFs) and related topics. Some geometric theorems are developed, and aspects of frame theory are used to gain insight into ETFs. We develop a projection ...
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 ...