The Fock Space and Related Bergman Type Integral Operators

Author

Ovidiu Furdui, Western Michigan University

Date of Award

6-2007

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Dr. John Srdjan Petrovic

Second Advisor

Dr. Yan-chun James Tung

Third Advisor

Dr. Paul Eenigenburg

Fourth Advisor

Dr. Jim Zhu

Abstract

In this thesis we study the boundedness of a general class of integral operators induced by the kernel functions of Fock spaces. More precisely, for a, b, and c real parameters we study the action of [Special characters omitted.] and [Special characters omitted.] on Lp ([Special characters omitted.] ,dv_s ), where dv_s ( z ) = [Special characters omitted.] is the Gaussian probability measure on [Special characters omitted.] . We prove that, when p > 1, respectively p = 1, these operators are bounded if and only if p satisfies a quadratic, respectively a linear, inequality. The operator S_a,b,c generalizes the classical Bergman projectionoperator [Special characters omitted.] which is bounded on L^p ([Special characters omitted.] , dv_t ) if and only if p = 2. We will also determine the norms of S_a,0,c and T_a,0,c on L^p ([Special characters omitted.] , dv_t ).

Access Setting

Dissertation-Open Access

Recommended Citation

Furdui, Ovidiu, "The Fock Space and Related Bergman Type Integral Operators" (2007). Dissertations. 862.
https://scholarworks.wmich.edu/dissertations/862