Global hypoelliptic vector fields in ultradifferentiable classes and normal forms

In this paper we prove that a global ω-hypoelliptic vector field on the torus Tn can be transformed by a Eω diffeomorphism of Tn into a vector field with constant coefficients which satisfy a Diophantine condition in terms of the weight function ω. Thereby, we extend previous work by Chen and Chi to...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2020-11, Vol.491 (1), p.124286, Article 124286
Main Author: Albanese, Angela A.
Format: Article
Language:English
Subjects:
Diophantine condition
Global hypoellipticity
Normal form
Ultradifferentiable classes
Vector field
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Summary:In this paper we prove that a global ω-hypoelliptic vector field on the torus Tn can be transformed by a Eω diffeomorphism of Tn into a vector field with constant coefficients which satisfy a Diophantine condition in terms of the weight function ω. Thereby, we extend previous work by Chen and Chi to a bigger scale of spaces, namely, in the setting of ultradifferentiable classes and ultradistributions of Beurling and Roumieu type.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2020.124286