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Simultaneous reduction of a family of commuting real vector fields and global hypoellipticity

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Abstract

In this paper we consider a family of commuting real vector fields on then-dimensional torus and show that it can be transformed into a family of constant vector fields provided that there is one of them which its transposed is globally hypoelliptic. We apply this result to prove global hypoellipticity for certain classes of sublaplacians.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de São Carlos, 13565-905, São Carlos, SP, Brazil

    Gerson Petronilho

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  1. Gerson Petronilho
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The author was partially supported by CNPq.

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Petronilho, G. Simultaneous reduction of a family of commuting real vector fields and global hypoellipticity. Isr. J. Math. 155, 81–92 (2006). https://doi.org/10.1007/BF02773949

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  • DOI: https://doi.org/10.1007/BF02773949

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