In this paper we prove that a global $omega$-hypoelliptic vector field on the torus $T^n$ can be transformed by a $mathcall{E}_omega}-diffeomorphism of $T^n$ into a vector field with constant coefficients which satisfy a Diophantine condition in terms of the weight function $omega$. 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.
Global hypoelliptic vector fields in ultradifferentiable classes and normal forms
Angela A. Albanese
Investigation
2020-01-01
Abstract
In this paper we prove that a global $omega$-hypoelliptic vector field on the torus $T^n$ can be transformed by a $mathcall{E}_omega}-diffeomorphism of $T^n$ into a vector field with constant coefficients which satisfy a Diophantine condition in terms of the weight function $omega$. 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.File in questo prodotto:
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