# Paley-Wiener properties for spaces of power series expansions

## TL;DR

This paper extends Paley-Wiener theorems to broader classes of power series expansions, providing new characterizations of Pilipović spaces and their distributions beyond previous low-order results.

## Contribution

It generalizes Paley-Wiener results in the Bargmann setting to larger classes of power series and characterizes all Pilipović spaces and their distributions.

## Key findings

- Extended Paley-Wiener results to broader power series classes
- Characterized all Pilipović spaces and their distributions
- Provided new insights beyond low-order cases

## Abstract

We extend Paley-Wiener results in the Bargmann setting deduced earlier by the author together with E. Nabizadeh and C. Pfeuffer to larger class of power series expansions. At the same time we deduce characterisations of all Pilipovi{\'c} spaces and their distributions (and not only of low orders as in the earlier work).