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

TL;DR

This paper introduces a discrete analog of Paley-Wiener spaces on the square lattice, providing a characterization and sampling results for these spaces of entire functions defined on a grid.

Contribution

It develops a Paley-Wiener type characterization and sampling theory for a new class of discrete entire functions on the square lattice.

Findings

Established a Paley-Wiener type theorem for discrete entire functions.

Proved sampling theorems for these discrete function spaces.

Connected discrete holomorphic functions to classical Paley-Wiener spaces.

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.