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Now showing items 21-30 of 66

#### 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: ...

#### 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} ...

#### 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 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 $\alpha-1/2$.

#### 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, ...

#### Zigzags of Finite, Bounded Posets and Monotone Near-Unanimity Functions and Jónsson Operations

(University of Waterloo, 2009-09-25)

We define the notion of monotone operations admitted by partially ordered sets,
specifically monotone near-unanimity functions and Jónsson operations. We then
prove a result of McKenzie's in [8] which states that if a ...

#### 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 ...

#### Contributions to the model theory of partial differential fields

(University of Waterloo, 2013-08-28)

In this thesis three topics on the model theory of partial differential fields are considered: the generalized Galois theory for partial differential fields, geometric axioms for the theory of partial differentially closed ...

#### Algebraic characterization of multivariable dynamics

(University of Waterloo, 2009-03-26)

Let X be a locally compact Hausdorﬀ space along with n proper continuous maps σ = (σ1 , · · · , σn ). Then the pair (X, σ) is called a dynamical system. To each system one can associate a universal operator algebra called ...

#### Degree Spectra of Unary relations on ω and ζ

(University of Waterloo, 2009-08-13)

Let X be a unary relation on the domain of (ω,<). The degree spectrum of X on (ω,<) is the set of Turing degrees of the image of X in all computable presentations of (ω,<). Many results are known about the types of degree ...