Fourier analysis for Denjoy–Carleman classes on the torus

Abstract

In the present article, we develop Fourier series for a family of classes of Romieu type of ultradifferentiable functions and ultradistributions on the torus, usually known as Denjoy-Carleman classes. In this setting, as applications, we extend the Greenfield-Wallach Theorem and, through a conjugation, we characterize global hypoellipticity for a class of systems of real vector fields of tube type.