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Globally hypoelliptic triangularizable systems of periodic pseudo‐differential operators

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  • Fernando de Ávila Silva

Abstract

This paper presents an investigation on the global hypoellipticity problem for a class of systems of pseudo‐differential operators on the torus. The approach consists in establishing conditions on the matrix symbol of the system such that it can be transformed into a suitable triangular form involving a nilpotent upper triangular matrix. Hence, the global hypoellipticity is studied by analyzing the behavior of the eigenvalues and their averages.

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  • Fernando de Ávila Silva, 2023. "Globally hypoelliptic triangularizable systems of periodic pseudo‐differential operators," Mathematische Nachrichten, Wiley Blackwell, vol. 296(6), pages 2293-2320, June.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:6:p:2293-2320
    DOI: 10.1002/mana.202100132
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    1. Adalberto Panobianco Bergamasco & Alberto Parmeggiani & Sérgio Luís Zani & Giuliano Angelo Zugliani, 2018. "Geometrical proofs for the global solvability of systems," Mathematische Nachrichten, Wiley Blackwell, vol. 291(16), pages 2367-2380, November.
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