Browsing Pure Mathematics by Title
Now showing items 83-102 of 165
-
MATRIX ALGEBRAS WITH A CERTAIN COMPRESSION PROPERTY I
(Elsevier, 2021-07-15)An algebra A of n × n complex matrices is said to be projection compressible if P AP is an algebra for all orthogonal projections P ∈ Mn(C). Analogously, A is said to be idempotent compressible if EAE is an algebra for all ... -
Maximal ideal space techniques in non-selfadjoint operator algebras
(University of Waterloo, 2013-04-26)The following thesis is divided into two main parts. In the first part we study the problem of characterizing algebras of functions living on analytic varieties. Specifically, we consider the restrictions M_V of the ... -
Maximal Operators in R^2
(University of Waterloo, 2007-08-13)A maximal operator over the bases $\mathcal{B}$ is defined as \[Mf(x) = \sup_{x \in B \in \mathcal{B}} \frac{1}{|B|}\int_B |f(y)|dy. \] The boundedness of this operator can be used in a number of applications including ... -
Mean Curvature Flow in Euclidean spaces, Lagrangian Mean Curvature Flow, and Conormal Bundles
(University of Waterloo, 2011-08-10)I will present the mean curvature flow in Euclidean spaces and the Lagrangian mean curvature flow. We will first study the mean curvature evolution of submanifolds in Euclidean spaces, with an emphasis on the case of ... -
Mind the GAP: Amenability Constants and Arens Regularity of Fourier Algebras
(University of Waterloo, 2023-08-28)This thesis aims to investigate properties of algebras related to the Fourier algebra $A(G)$ and the Fourier-Stieltjes algebra $B(G)$, where $G$ is a locally compact group. For a Banach algebra $\cA$ there are two natural ... -
The Model Theory of Algebraically Closed Fields
(University of Waterloo, 2000)Model theory can express properties of algebraic subsets of complex n-space. The constructible subsets are precisely the first order definable subsets, and varieties correspond to maximal consistent collections of ... -
Moment Polynomials for the Riemann Zeta Function
(University of Waterloo, 2009-01-21)In this thesis we calculated the coefficients of moment polynomials of the Riemann zeta function for k= 4, 5, 6...13 using cubic acceleration, which is an improved method from quadratic acceleration. We then numerically ... -
The Mordell-Lang Theorem from the Zilber Dichotomy
(University of Waterloo, 2010-04-30)We present a largely self-contained exposition of Ehud Hrushovski's proof of the function field Mordell-Lang conjecture beginning from the Zilber Dichotomy for differentially closed fields and separably closed fields. Our ... -
Multiplicities of Linear Recurrence Sequences
(University of Waterloo, 2006)In this report we give an overview of some of the major results concerning the multiplicities of linear recurrence sequences. We first investigate binary recurrence sequences where we exhibit a result due to Beukers and ... -
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 $\alpha-1/2$.