Electronic Theses and Dissertations

Identifier

973

Date

2013

Document Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematical Sciences

Concentration

Mathematics

Committee Chair

James Jamison

Committee Member

Fernanda Botelho

Committee Member

Pei-Kee Lin

Committee Member

Thomas Hagen

Abstract

We look at unbounded hermitian operators on Kolaski spaces with derivatives in a smooth space, $H_N$. We find the generator of one parameter groups of isometries on Kolaski spaces and provide spectral properties of the generator. We apply this result to the $S^p(D)$ spaces using results from Berkson and Porta on $H^p$ spaces. We then consider the vector valued space $H^p_{mathcal{H}}$ and determine the bounded hermitian operators and provide results if a particular group of disk automorphisms is used. In the second part we find that the generalized bi-circular projections on $H^p(mathbb{T}^2)$ are given by the average of the identity and a reflection. We then find when the average of two isometries on $S^p_K$ is a projection. This result leads to a corollary that the average of two isometries on $H^p(D)$ is a generalized bi-circular projection.

Comments

Data is provided by the student.

Library Comment

Dissertation or thesis originally submitted to the local University of Memphis Electronic Theses & dissertation (ETD) Repository.

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