Perturbations by lower order terms do not destroy the global hypoellipticity of certain systems of pseudodifferential operators defined on torus

Igor Ambo Ferra and Gerson Petronilho

Mathematische Nachrichten, 2023, vol. 296, issue 7, 2780-2794

Abstract: We introduce a new class of smooth pseudodifferential operators on the torus whose calculus allows us to show that global hypoellipticity with a finite loss of derivatives of certain systems of pseudodifferential operators is stable under perturbations by lower order systems of pseudodifferential operators whose order depends on the loss of derivatives. We also present some applications.

Date: 2023
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https://doi.org/10.1002/mana.202000409

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