Date of Award
Winter 1994
Abstract
Let ${\cal H}$ be a functional Hilbert space of analytic functions on a complex domain $\Omega,$ with the normalized reproducing kernel function $k\sb{z},\ z\in\Omega.$ If A is a linear map of ${\cal H}$ into itself, the Berezin symbol, A, of A is defined on $\Omega$ by $\tilde{A}(z) = \langle Ak\sb{z},\ k\sb{z}\rangle.$ The purpose of this research is to study how the properties of an operator are reflected in the properties of its Berezin symbol. In summary, I have (1) studied the properties of the Berezin symbol as a complex-valued function; (2) characterized multiplication operators, induced by a multiplier of ${\cal H},$ using the multiplicative property of the map $A\mapsto\tilde{A};$ (3) expressed the boundedness and compactness properties of certain operators in terms of their Berezin symbols; and (4) characterized the set of multipliers as the set of analytic Berezin symbols of bounded operators.
Document Type
Dissertation
First Advisor
Eric Nordgren
Department or Program
Mathematics
Degree Name
Doctor of Philosophy
Recommended Citation
Kilic-Bahi, Semra, "On the Berezin symbol" (1994). Doctoral Dissertations. 1818.
https://scholars.unh.edu/dissertation/1818