Global and Partial Fourier Series for Denjoy-Carleman Classes on the Torus

Abstract

In this work, we develop Fourier Analysis for a family of classes of ultradifferentiable functions of Romieu type on the torus, usually known as Denjoy-Carleman classes. Then we are able to apply our results in order to generalize some results whose proofs rely almost exclusively on Fourier Series, such as the Greenfield-Wallach Theorem.