Globally hypoelliptic triangularizable systems of periodic pseudo‐differential operators

Fernando de Ávila Silva

Mathematische Nachrichten, 2023, vol. 296, issue 6, 2293-2320

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.

Date: 2023
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https://doi.org/10.1002/mana.202100132

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