Geodesic
Fourier analysis for Denjoy–Carleman classes on the torus
Bruno de Lessa Victor1
1 Universidade Federal do Paraná, Curitiba, Departamento de Matemática
Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 869-895

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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.
Keywords: Ultradifferentiable classes, Fourier series, global hypoellipticity

Bruno de Lessa Victor 1

1 Universidade Federal do Paraná, Curitiba, Departamento de Matemática 
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Bruno de Lessa Victor. Fourier analysis for Denjoy–Carleman classes on the torus. Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 869-895. http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a16/