Search
Now showing items 1-10 of 14
Norms of Composition Operators on the Hardy Space
This thesis covers Hilbert spaces, Hardy spaces, their properties, and composition operators.
Chaos and the Dynamics of Quadratic Mappings
The immediate aim of this paper is to systematically investigate dynamical systems governed by a certain class of difference equations. The results obtained do not, however, constitute an isolated piece in a sprawling ...
An Elementary Theorem-Proving Program
My goal is to write a theorem-proving assistant that can , to s ome extent, take a hypothesis (that works on IF-THEN rules) and make some progress toward a realizable goal. However, since I need a more concrete problem ...
Compressions of Linear Operators Yielding a Single Point Numerical Range
This thesis will focus on finding subspaces M such that the compression of T to M, denoted TM, has a single point numerical range. . . . The motivation for finding such subspaces lies in a theorem from quantum coding ...
Chaos and Linearity
Mathematically, one may define chaos in relation to the behavior of discrete dynamical systems, i.e., the behavior of operators (functions) under iteration. R. Devaney, in his book An Introduction to Chaotic Dynamical ...
Rado's Selection Principle: Equivalences and Applications
Rado's Selection Principle is a combinatorial theorem which allows the characterization of infinite objects (e.g. graphs, groups, partially-ordered sets) based on the characterization of their finite subparts. That is, a ...
Sex, Guns, and Theorems; The Legacy of Evariste Galois
Only ignorance of history can allow one to see mathematicians as those who lead boring, uneventful lives, and a brief look at the career of the French mathematician Evariste Galois (1811 - 1832) will put any skeptic to ...
Rotation Remainders
An object in mathematics that first appears for the sake of amusement can demonstrate deep connections with well-known questions about numbers. Consider an array of numbers formed by a rotating queue: starting with just ...
Julia Sets: An Introduction to Chaos in the Plane
In this paper we introduce the reader to a family of functions which give rise to Julia sets. Making their home in the complex plane, these sets exhibit many interesting properties, including chaotic dynamics . The aesthetic ...
Compressing Operators to Obtain Single-Point Numerical Ranges
We are all familiar with vector spaces and their basic properties. We understand linear operators, dot products, and maybe even norms. What the reader may not be as familiar with, however, is the concept of numerical range. ...