Global and Partial Fourier Series for Denjoy-Carleman Classes on the Torus
Analysis of PDEs
2019-10-29 v1
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.
Keywords
Cite
@article{arxiv.1910.12605,
title = {Global and Partial Fourier Series for Denjoy-Carleman Classes on the Torus},
author = {Alexandre Kirilov and Bruno de Lessa Victor},
journal= {arXiv preprint arXiv:1910.12605},
year = {2019}
}