Browsing Pure Mathematics by Title
Now showing items 92-111 of 165
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Nevanlinna-Pick Spaces and Dilations
(University of Waterloo, 2016-07-12)The majority of this thesis is devoted to the study of Nevanlinna-Pick spaces and their multiplier algebras. These spaces are Hilbert function spaces in which a version of the Nevanlinna-Pick interpolation theorem from ... -
Non-Isotopic Symplectic Surfaces in Products of Riemann Surfaces
(University of Waterloo, 2006)<html> <head> <meta http-equiv="Content-Type" content="text/html;charset=iso-8859-1"> </head> Let Σ<em><sub>g</sub></em> be a closed Riemann surface of genus <em>g</em>. Generalizing Ivan Smith's construction, ... -
The Normal Distribution of ω(φ(m)) in Function Fields
(University of Waterloo, 2008-01-28)Let ω(m) be the number of distinct prime factors of m. A celebrated theorem of Erdös-Kac states that the quantity (ω(m)-loglog m)/√(loglog m) distributes normally. Let φ(m) be Euler's φ-function. Erdös and Pomerance ... -
Normal operators with highly incompatible off-diagonal corners
(Polish Academy of Sciences, 2020-05-25)Let H be a complex, separable Hilbert space, and B(H) denote the set of all bounded linear operators on H. Given an orthogonal projection P∈B(H) and an operator D∈B(H), we may write D=[D1D3D2D4] relative to the decomposition ... -
Notions of Complexity Within Computable Structure Theory
(University of Waterloo, 2023-08-28)This thesis covers multiple areas within computable structure theory, analyzing the complexities of certain aspects of computable structures with respect to different notions of definability. In chapter 2 we use a new ... -
The O'Nan-Scott Theorem for Finite Primitive Permutation Groups, and Finite Representability
(University of Waterloo, 2009-08-06)The O'Nan-Scott Theorem classifies finite primitive permutation groups into one of five isomorphism classes. This theorem is very useful for answering questions about finite permutation groups since four out of the five ... -
OFF-DIAGONAL CORNERS OF SUBALGEBRAS OF L(Cn)
(Elsevier, 2020-12-15)Let n ∈ N, and consider Cn equipped with the standard inner product. Let A ⊆ L(Cn) be a unital algebra and P ∈ L(Cn) be an orthogonal projection. The space L := P ⊥A|ran P is said to be an off-diagonal corner of A, and L ... -
On a Question of Wintner Concerning the Sequence of Integers Composed of Primes from a Given Set
(University of Waterloo, 2007-09-27)We answer to a Wintner's question concerning the sequence of integers composed of primes from a given set. The results generalize and develop the answer to Wintner’s question due to Tijdeman. -
On Amenability Properties and Coideals of Quantum Groups
(University of Waterloo, 2022-07-27)We study amenability type properties of locally compact quantum groups and subobjects of quantum groups realized as submodules of their von Neumann algebras. An important class of such subobjects are the coideals, which ... -
On Asynchronous Interference Channels
(University of Waterloo, 2016-11-15)In the first part of the thesis, a decentralized wireless network of separate transmitter-receiver pairs is studied where there is no central controller to assign the resources to the users and users do not explicitly ... -
On Convolution Squares of Singular Measures
(University of Waterloo, 2010-08-25)We prove that if $1 > \alpha > 1/2$, then there exists a probability measure $\mu$ such that the Hausdorff dimension of its support is $\alpha$ and $\mu*\mu$ is a Lipschitz function of class $\alpha-1/2$. -
On Diagonal Acts of Monoids
(University of Waterloo, 2007-08-30)In this paper we discuss what is known so far about diagonal acts of monoids. The first results that will be discussed comprise an overview of some work done on determining whether or not the diagonal act can be finitely ... -
On fixed points of self maps of the free ball
(Elsevier, 2018-07-01)In this paper, we study the structure of the fixed point sets of noncommutative self maps of the free ball. We show that for such a map that fixes the origin the fixed point set on every level is the intersection of the ... -
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 ...