Paley-Wiener properties for spaces of entire functions

TL;DR

This paper extends Paley-Wiener theorems to the Bargmann setting, providing characterizations of Pilipovi{\'c} spaces of low orders and generalizing previous results on Gr{"o}chenig test function spaces.

Contribution

It introduces new Paley-Wiener characterizations in the Bargmann setting for Pilipovi{\'c} spaces, broadening the understanding of entire function spaces.

Findings

Characterization of Pilipovi{\'c} spaces of low orders

Extension of Gr{"o}chenig test function space results

New Paley-Wiener theorems in the Bargmann setting

Abstract

We deduce Paley-Wiener results in the Bargmann setting, which give characterisations of Pilipovi{\'c} spaces of low orders, extending the characterisation of a Gr{\"o}chenig test function space, deduced earlier by the third author.