Browsing Pure Mathematics by Title
Now showing items 127-146 of 165
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Ranges of vector states on irreducible operator semigroups
(Springer, 2016)Let 𝜑 be a linear functional of rank one acting on an irreducible semigroup S of operators on a finite- or infinite-dimensional Hilbert space. It is a well-known and simple fact that the range of 𝜑 cannot be a singleton. ... -
Rational approximations on smooth rational surfaces
(University of Waterloo, 2019-08-09)In this thesis, we study a conjecture made by D. McKinnon about rational approximations to rational points in algebraic varieties. The conjecture states that if a rational point P on a variety X lies on a rational curve, ... -
Recurrence in Algebraic Dynamics
(University of Waterloo, 2020-07-28)The Dynamical Mordell--Lang Conjecture states that if a polynomial orbit has infinite intersection with a closed set in an algebraic variety, then the intersection must occur periodically. Although this problem is unsolved ... -
Reducibility of operator semigroups and values of vector states
(Springer, 2017-08-01)Let S be a multiplicative semigroup of bounded linear operators on a complex Hilbert space H, and let Ω be the range of a vector state on S so that Ω = {⟨Sξ, ξ⟩ : S ∈ S} for some fixed unit vector ξ ∈ H. We study the ... -
Reductions and Triangularizations of Sets of Matrices
(University of Waterloo, 2006)Families of operators that are triangularizable must necessarily satisfy a number of spectral mapping properties. These necessary conditions are often sufficient as well. This thesis investigates such properties in ... -
Regular Dilation on Semigroups
(University of Waterloo, 2018-08-07)Dilation theory originated from Sz.Nagy's celebrated dilation theorem which states that every contractive operator has an isometric dilation. Regular dilation is one of many fruitful directions that aims to generalize ... -
Representations of Operator Algebras
(University of Waterloo, 2012-05-11)The following thesis is divided into two main chapters. In Chapter 2 we study isometric representations of product systems of correspondences over the semigroup 𝐍ᵏ which are minimal dilations of finite dimensional, fully ... -
Residual finite dimensionality and representations of amenable operator algebras
(Elsevier, 2019-04-15)We consider a version of a famous open problem formulated by Kadison, asking whether bounded representations of operator algebras are automatically completely bounded. We investigate this question in the context of amenable ... -
Semicrossed Products, Dilations, and Jacobson Radicals
(University of Waterloo, 2017-08-18)We compute the C*-envelope of the isometric semicrossed product of a C*-algebra arising from number theory by the multiplicative semigroup of a number ring R, and prove that it is isomorphic to T[R], the left regular ... -
Semistable rank 2 co-Higgs bundles over Hirzebruch surfaces
(University of Waterloo, 2015-08-07)It has been observed by S. Rayan that the complex projective surfaces that potentially admit non-trivial examples of semistable co-Higgs bundles must be found at the lower end of the Enriques-Kodaira classification. ... -
Series-Parallel Posets and Polymorphisms
(University of Waterloo, 2018-09-04)We examine various aspects of the poset retraction problem for series-parallel posets. In particular we show that the poset retraction problem for series-parallel posets that are already solvable in polynomial time are ... -
Settling Time Reducibility Orderings
(University of Waterloo, 2010-04-28)It is known that orderings can be formed with settling time domination and strong settling time domination as relations on c.e. sets. However, it has been shown that no such ordering can be formed when considering computation ... -
Sidon and Kronecker-like sets in compact abelian groups
(University of Waterloo, 2019-06-07)Let $G$ be a compact abelian group and $\Ga$ be its discrete dual group. In this thesis we study various types of interpolation sets. A subset $E \subset \Ga$ is Sidon if every bounded function on $E$ can be interpolated ... -
Some additive results in F_q[t]
(University of Waterloo, 2015-08-27)We collected several results in integers of additive number theory and translated to results in F_q[t]. The results we collected are related to slim exceptional sets and the asymptotic formula in Waring's problem, a ... -
Some aspects of Cantor sets
(University of Waterloo, 2014-03-28)For every positive, decreasing, summable sequence $a=(a_i)$, we can construct a Cantor set $C_a$ associated with $a$. These Cantor sets are not necessarily self-similar. Their dimensional properties and measures have been ... -
Some Functional Equations Connected with the Utility of Gains and Losses
(University of Waterloo, 2002)The behavioral properties shown by people when they make selections between different choices will be studied. Based on empirical and logical data a mathematical axiomatic model is built. D. Luce is a major ... -
Some Problems in Multiplicative and Additive Number Theory
(University of Waterloo, 2020-07-27)In this thesis, we obtain several results in number theory. Let $k\geqslant 1$ be a natural number and $\omega_k(n)$ denote the number of distinct prime factors of a natural number $n$ with multiplicity $k$. We estimate ... -
Some results on binary forms and counting rational points on algebraic varieties
(University of Waterloo, 2016-08-17)In this thesis we study several problems related to the representation of integers by binary forms and counting rational points on algebraic varieties. In particular, we establish an asymptotic formula for $R_F(Z)$, the ... -
Sparse Automatic Sets
(University of Waterloo, 2020-11-26)The theory of automatic sets and sequences arises naturally in many different areas of mathematics, notably in the study of algebraic power series in positive characteristic, due to work of Christol, and in Derksen's ... -
A spatial version of Wedderburn’s Principal Theorem
(Taylor & Francis, 2015)In this article we verify that ‘Wedderburn’s Principal Theorem’ has a particularly pleasant spatial implementation in the case of cleft subalgebras of the algebra of all linear transformations on a finite-dimensional vector ...