Real Paley-Wiener theorems in spaces of ultradifferentiable functions
Functional Analysis
2023-04-18 v1
Abstract
We develop real Paley-Wiener theorems for classes of ultradifferentiable functions and related -spaces in the spirit of Bang and Andersen for the Schwartz class. We introduce results of this type for the so-called Gabor transform and give a full characterization in terms of Fourier and Wigner transforms for several variables of a Paley-Wiener theorem in this general setting, which is new in the literature. We also analyze this type of results when the support of the function is not compact using polynomials. Some examples are given.
Keywords
Cite
@article{arxiv.1902.02745,
title = {Real Paley-Wiener theorems in spaces of ultradifferentiable functions},
author = {Chiara Boiti and David Jornet and Alessandro Oliaro},
journal= {arXiv preprint arXiv:1902.02745},
year = {2023}
}