Now showing items 1-10 of 66
Free semigroup algebras and the structure of an isometric tuple
(University of Waterloo, 2011-06-28)
An n-tuple of operators V=(V_1,…,V_n) acting on a Hilbert space H is said to be isometric if the corresponding row operator is an isometry. A free semigroup algebra is the weakly closed algebra generated by an isometric ...
The Cohomology Ring of a Finite Abelian Group
(University of Waterloo, 2013-01-25)
The cohomology ring of a finite cyclic group was explicitly computed by Cartan and Eilenberg in their 1956 book on Homological Algebra. It is surprising that the cohomology ring for the next simplest example, that of a ...
Harmonic analysis of Rajchman algebras
(University of Waterloo, 2010-08-31)
Abstract harmonic analysis is mainly concerned with the study of locally compact groups, their unitary representations, and the function spaces associated with them. The Fourier and Fourier-Stieltjes algebras are two of ...
Generalisations of Roth's theorem on finite abelian groups
(University of Waterloo, 2012-12-18)
Roth's theorem, proved by Roth in 1953, states that when A is a subset of the integers [1,N] with A dense enough, A has a three term arithmetic progression (3-AP). Since then the bound originally given by Roth has been ...
The Lang-Trotter conjecture for Drinfeld modules
(University of Waterloo, 2011-08-22)
In 1986, Gupta and Murty proved the Lang-Trotter conjecture in the case of elliptic curves having complex multiplication, conditional on the generalized Riemann hypothesis. That is, given a non-torsion point P∈E(ℚ), they ...
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 ...
Upper Bounds for the Number of Integral Points on Quadratic Curves and Surfaces
(University of Waterloo, 2010-04-27)
We are interested in investigating the number of integral points on quadrics. First, we consider non-degenerate plane conic curves defined over Z. In particular we look at two types of conic sections: hyperbolas with ...
The Fourier algebra of a locally trivial groupoid
(University of Waterloo, 2012-01-10)
The goal of this thesis is to define and study the Fourier algebra A(G) of a locally compact groupoid G. If G is a locally compact group, its Fourier-Stieltjes algebra B(G) and its Fourier algebra A(G) were defined by ...
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 ...
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.