Global hypoellipticity on time-periodic Gelfand-Shilov spaces via non-discrete Fourier analysis

TL;DR

This paper characterizes time-periodic Gelfand-Shilov spaces using Fourier transforms and establishes conditions for global regularity of certain differential operators within this framework.

Contribution

It introduces a Fourier-based characterization of these spaces and provides necessary and sufficient conditions for the global regularity of specific differential operators.

Findings

Characterization of time-periodic Gelfand-Shilov spaces via Fourier transforms.

Necessary and sufficient conditions for global regularity of constant-coefficient differential operators.

Application to first-order tube-type operators.

Abstract

In this paper, we provide a characterization of the time-periodic Gelfand-Shilov spaces, as introduced by F. de \'Avila Silva and M. Cappiello [J. Funct. Anal., 282(9):29, 2022], through the asymptotic behaviour of both the Euclidean and periodic partial Fourier transforms of their elements. As an application, we establish necessary and sufficient conditions for global regularity -- within this framework -- for a broad class of constant-coefficient differential operators, as well as for first-order tube-type operators.