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arXiv · 1910.12605

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

Alexandre Kirilov·Bruno de Lessa Victor
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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.

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Alexandre Kirilov, Bruno de Lessa Victor. 2019-10-28. Global and Partial Fourier Series for Denjoy-Carleman Classes on the Torus. https://arxiv.org/abs/1910.12605

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