Fourier analysis for Denjoy–Carleman classes on the torus

Authors

  • Bruno de Lessa Victor Universidade Federal do Paraná, Curitiba, Departamento de Matemática

Keywords:

Ultradifferentiable classes, Fourier series, global hypoellipticity

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.
Section
Articles

Published

2021-08-04

How to Cite

Victor, B. de L. (2021). Fourier analysis for Denjoy–Carleman classes on the torus. Annales Fennici Mathematici, 46(2), 869–895. Retrieved from https://afm.journal.fi/article/view/110606