Paley-Wiener spaces of discrete entire functions on Z^2

Matteo Monti

Session: General

Keywords: Paley--Wiener, discrete entire functions

TL;DR: tl;dr

Abstract:

In this talk I will present a Paley--Wiener type theorem for the class of discrete entire functions on $\mathbb Z^2$. Similarly to the continuous case, I will show how a suitable exponential growth condition of a discrete entire function $F$ is interlinked with the support of the Fourier transform of the restriction of $F$ to $\mathbb Z\times \{0\}$.

I will then define some reproducing kernel Hilbert spaces $PW_\alpha$. For such spaces I will provide a sampling result. Namely, I will provide sufficient conditions to reconstruct the function on $\mathbb Z^2$ starting only from the sampling of the function on a proper subsets of $\mathbb Z$.

This is a joint work with Alessandro Monguzzi.

Submission Number: 133