Date of Award
Doctor of Philosophy (PhD)
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.
Chair and Committee
James Gill, Gregory Knese, Richard Rochberg, Xiang Tang,
Chu, Cheng, "Three Problems in Operator Theory and Complex Analysis" (2016). Arts & Sciences Electronic Theses and Dissertations. 773.