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

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

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,...

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Bibliographic Details
Main Authors: Kirilov, Alexandre, Victor, Bruno de Lessa
Format: Journal Article
Language:English
Published: 28-10-2019
Subjects:
Mathematics - Analysis of PDEs
Online Access:Get full text
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Summary: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.
DOI:10.48550/arxiv.1910.12605