Date of Award

Spring 1993

Project Type

Dissertation

Program or Major

Mathematics

Degree Name

Doctor of Philosophy

First Advisor

Eric Nordgren

Abstract

In this paper we consider the Hankel operators from two points of view. On one hand the Hankel operator is induced by the coefficient sequence $a\sb0,a\sb1,a\sb2,\...$ and operates on a Hilbert space $H\sp2(\beta)$ with $\Sigma\sbsp{n=0}{\infty}\ \beta(n)\sp2 < \infty.$ In this situation we can find necessary conditions and sufficient conditions for the Hankel operator to be bounded. However, with compactness and Hilbert-Schmidt we can get only sufficient conditions. On the other hand we look at the Hankel operator $H\sb{f,\alpha}$ and little Hankel operator $h\sb{f,\alpha},$ with symbol function f, that operates on a weighted Bergman space. In this case we can determine bounded, compact, Hilbert Schmidt, or trace class operators of the Hankel operator $H\sb{f}$ and $h\sb{f,\alpha}.$ We also give a good estimate of bounded norm of little Hankel operators with a particular symbol function $f = z\bar g$ where g is in the Bloch space.

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