Abstract

This thesis concerns three distinct problems in operator theory and complex analysis. In Chapter 2, we study the following problem: On the Hardy space H^2, when is the product of a Hankel operator and a Toeplitz operator compact? We give necessary and sucient conditions for when such a product H_fT_g is compact. In Chapter 3, we discuss hyponormal Toeplitz operators. We show that for those operators, there exists a lower bound for the area of the spectrum. This extends the known estimate for the spectral area of Toeplitz operators with an analytic symbol. This part is joint work with Dmitry Khavinson. In Chapter 4, we study the Bohr radius R_n for the class of complex polynomials of degree at most n. Bohr's theorem showed that R_n goes to 1/3 as n tends to infinity. We are interested in the rate of convergence and proved an asymptotic formula that was conjectured by R. Fournier in 2008.

Committee Chair

John McCarthy

Committee Members

James Gill, Gregory Knese, Richard Rochberg, Xiang Tang,

Comments

Permanent URL: https://doi.org/10.7936/K7HH6HCG

Degree

Doctor of Philosophy (PhD)

Author's Department

Mathematics

Author's School

Graduate School of Arts and Sciences

Document Type

Dissertation

Date of Award

Spring 5-15-2016

Language

English (en)

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Mathematics Commons

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