Electronic Theses and Dissertations

Identifier

973

Date

2013

Date of Award

11-25-2013

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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