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

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  • Igor Ambo Ferra
  • Gerson Petronilho

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.

Suggested Citation

  • Igor Ambo Ferra & Gerson Petronilho, 2023. "Perturbations by lower order terms do not destroy the global hypoellipticity of certain systems of pseudodifferential operators defined on torus," Mathematische Nachrichten, Wiley Blackwell, vol. 296(7), pages 2780-2794, July.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:7:p:2780-2794
    DOI: 10.1002/mana.202000409
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