On discrete holomorphic Paley-Wiener spaces and sampling on the square lattice

Abstract

We consider a reproducing kernel Hilbert space of discrete entire functions on the square lattice ${\mathbb{Z}}^2$ inspired by the classical Paley-Wiener space of entire functions of exponential growth in the complex plane. For such space we provide a Paley-Wiener type characterization and a sampling result.

24 pages. Corrected minor typos in the proofs of Theorems 1.3 and 1.5. The main results and their proofs remain unchanged