Global hypoellipticity, global solvability and normal form for a class of real vector fields on a torus and application

Petronilho, G.

doi:10.1090/S0002-9947-2011-05359-6

Global hypoellipticity, global solvability and normal form for a class of real vector fields on a torus and application
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Trans. Amer. Math. Soc. 363 (2011), 6337-6349 Request permission

Abstract:

The main purpose of this paper is to present a class of real vector fields defined on a torus for which the concepts of global hypoellipticity and global smooth solvability are equivalent. Furthermore, such a vector field is globally hypoelliptic if and only if its adjoint is globally hypoelliptic, and therefore we can reduce it to its normal form. As an application, we study global $C^\infty$ solvability for certain classes of sub-Laplacians.

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