Browsing Pure Mathematics by Title
Now showing items 105-124 of 165
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On Hopf Ore Extensions and Zariski Cancellation Problems
(University of Waterloo, 2020-04-29)In this thesis, we investigate Ore extensions of Hopf algebras and the Zariski Cancellation problem for noncommutative rings. In particular, we improve upon the existing conditions for when $T=R[x; \sigma, \delta]$ is a ... -
On selfadjoint extensions of semigroups of partial isometries
(American Mathematical Society, 2016)Let S be a semigroup of partial isometries acting on a complex, infinite- dimensional, separable Hilbert space. In this paper we seek criteria which will guarantee that the selfadjoint semigroup T generated by S consists ... -
On the Dynamical Wilf-Zeilberger Problem
(University of Waterloo, 2022-08-15)In this paper, we give an algorithmic solution to a dynamical analog of the problem of certifying combinatorial identities by Wilf-Zeilberger pairs. Given two sequences generated in a dynamical setting, we calculate an ... -
On the Erdös-Turán conjecture and related results
(University of Waterloo, 2011-08-29)The Erdös-Turán Conjecture, posed in 1941 in, states that if a subset B of natural numbers is such that every positive integer n can be written as the sum of a bounded number of terms from B, then the number of such ... -
On the local positivity of line bundles on algebraic surfaces
(University of Waterloo, 2015-01-09)In this thesis, we define a measure for how `positive' an effective line bundle is at a point on a variety, and prove that it is linear on the numerically effective subcone on a smooth, complete, toric surface. -
On the Modular Theory of von Neumann Algebras
(University of Waterloo, 2010-09-17)The purpose of this thesis is to provide an exposition of the \textit{modular theory} of von Neumann algebras. The motivation of the theory is to classify and describe von Neumann algebras which do not admit a trace, and ... -
On the Representation Theory of Semisimple Lie Groups
(University of Waterloo, 2010-08-30)This thesis is an expository account of three central theorems in the representation theory of semisimple Lie groups, namely the theorems of Borel-Weil-Bott, Casselman-Osborne and Kostant. The first of these realizes all ... -
On the Similarity of Operator Algebras to C*-Algebras
(University of Waterloo, 2006)This is an expository thesis which addresses the requirements for an operator algebra to be similar to a <em>C</em>*-algebra. It has been conjectured that this similarity condition is equivalent to either amenability ... -
On the structure of invertible elements in certain Fourier-Stieltjes algebras
(University of Waterloo, 2021-08-27)Let $G$ be a locally compact group. The Fourier-Stieltjes and Fourier algebras, $B(G)$ and $A(G)$ are defined by Eymard to act as dual objects of the measure and group algebras, $M(G)$ and $L^1(G)$, in a sense generalizing ... -
On the Structure of Nonnegative Semigroups of Matrices
(University of Waterloo, 2009-08-18)The results presented here are concerned with questions of decomposability of multiplicative semigroups of matrices with nonnegative entries. Chapter 1 covers some preliminary results which become useful in the remainder ... -
On Transcendence of Irrationals with Non-eventually Periodic b-adic Expansions
(University of Waterloo, 2010-05-18)It is known that almost all numbers are transcendental in the sense of Lebesgue measure. However there is no simple rule to separate transcendental numbers from algebraic numbers. Today research in this direction is about ... -
Operator Spaces and Ideals in Fourier Algebras
(University of Waterloo, 2008-08-11)In this thesis we study ideals in the Fourier algebra, A(G), of a locally compact group G. For a locally compact abelian group G, necessary conditions for a closed ideal in A(G) to be weakly complemented are given, ... -
Operator Theoretic Methods in Nevanlinna-Pick Interpolation
(University of Waterloo, 2009-03-31)This Master's thesis will develops a modern approach to complex interpolation problems studied by Carath\'{e}odory, Nevanlinna, Pick, and Schur in the early $20^{th}$ century. The fundamental problem to solve is as follows: ... -
OPERATORS WHICH ARE POLYNOMIALLY ISOMETRIC TO A NORMAL OPERATOR
(American Mathematical Society, 2020-01-15)Let H be a complex, separable Hilbert space and B(H) denote the algebra of all bounded linear operators acting on H. Given a unitarily-invariant norm k · ku on B(H) and two linear operators A and B in B(H), we shall say ... -
Para-Holomorphic Algebroids and Para-Complex Connections
(University of Waterloo, 2021-12-17)The goal of this paper is to develop the theory of Courant algebroids with integrable para-Hermitian vector bundle structures by invoking the theory of Lie bialgebroids. We consider the case where the underlying manifold ... -
A Parallel Study of the Fock Space Approach to Classical and Free Brownian Motion
(University of Waterloo, 2017-08-28)The purpose of this thesis is to elaborate the similarities between the classical and the free probability by means of developing the chaos decomposition of stochastic integrals driven by Brownian motion and its free ... -
Pick Interpolation and the Distance Formula
(University of Waterloo, 2012-05-09)The classical interpolation theorem for the open complex unit disk, due to Nevanlinna and Pick in the early 20th century, gives an elegant criterion for the solvability of the problem as an eigenvalue problem. In the 1960s, ... -
Posets of Non-Crossing Partitions of Type B and Applications
(University of Waterloo, 2007-10-19)The thesis is devoted to the study of certain combinatorial objects called \emph{non-crossing partitions}. The enumeration properties of the lattice ${\textsf{NC$^{\textsf{\,A}}$(n)}}\,$ of \emph{non-crossing partitions} ... -
Problems in Combinatorial and Analytic Number Theory
(University of Waterloo, 2018-08-01)We focus on three problems in number theory. The first problem studies the random Fibonacci tree, which is an infinite binary tree with non-negative integers at each node. The root consists of the number 1 with a single ... -
The Prouhet-Tarry-Escott problem
(University of Waterloo, 2013-01-15)Given natural numbers n and k, with n>k, the Prouhet-Tarry-Escott (PTE) problem asks for distinct subsets of Z, say X={x_1,...,x_n} and Y={y_1,...,y_n}, such that x_1^i+...+x_n^i=y_1^i+...+y_n^i\] for i=1,...,k. ...