Global Denjoy–Carleman hypoellipticity for a class of systems of complex vector fields and perturbations

We characterize global Denjoy–Carleman hypoellipticity for the family of systems acting on the torus T t N × T x given by L j = ∂ ∂ t j + a j ( t j ) + i b j ( t j ) ∂ ∂ x + λ j , where a j , b j are real-valued 2 π -periodic elements of the classes and j = 1 , 2 , … , N .

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Bibliographic Details
Published in:Annali di matematica pura ed applicata 2021-08, Vol.200 (4), p.1367-1398
Main Authors: de Lessa Victor, Bruno, Arias Junior, Alexandre
Format: Article
Language:English
Subjects:
Fields (mathematics)
Mathematics
Mathematics and Statistics
Perturbation
Toruses
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Summary:We characterize global Denjoy–Carleman hypoellipticity for the family of systems acting on the torus T t N × T x given by L j = ∂ ∂ t j + a j ( t j ) + i b j ( t j ) ∂ ∂ x + λ j , where a j , b j are real-valued 2 π -periodic elements of the classes and j = 1 , 2 , … , N .
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-020-01041-x