Spaces of Entire Functions in C^n+1

A renowned space of entire functions of one complex variable is the Paley–Wiener space P W A , that is, the space of entire functions of exponential type A whose restriction to the real line is square integrable. After recalling some basic properties of P W A I will present a generalization of this space in several complex variables. In particular, I will consider entire functions which satisfy a suitable exponential growth condition and whose restriction to the boundary of the Siegel half-space satisfy some integrability conditions. Time permitting, I will provide a Paley–Wiener type characterization and a sampling result. This is a joint work in progress with Marco Peloso and Maura Salvatori.