Fock spaces.

Abstract

Banach spaces of analytic functions such as the Hardy spaces and the Bergman spaces have been well investigated in the past half century. However, basic facts concerning Fock spaces remain scattered throughout literature. In this thesis we detail the basic properties of Fock spaces, including polynomial approximation, dual spaces, and boundedness of the Bergman projection. Using these basic properties we can obtain new results concerning Taylor coefficients of functions in Fock spaces. We also discuss interpolating and sampling sets in Fock spaces, which have been characterized in terms of certain uniform densities by Seip and Wallsten. Additional formulations of interpolating and sampling sets are developed. An example is constructed to show that an interpolating set in Fock spaces is not necessarily a zero set, which contrasts with the situation in Hardy and Bergman spaces.