Perturbations of globally hypoelliptic operators on closed manifolds

  • Fernando de Ávila Silva

    Universidade Federal do Paraná, Curitiba, Brazil
  • Alexandre Kirilov

    Universidade Federal do Paraná, Curitiba, Brazil
Perturbations of globally hypoelliptic operators on closed manifolds cover

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Abstract

Analyzing the behavior at infinity of the sequence of eigenvalues given by matrix symbol of a invariant operator with respect to a fixed elliptic operator, we obtain necessary and sufficient conditions to ensure that perturbations of globally hypoelliptic operators continue to have this property. As an application, we recover classical results about perturbations of constant vector fields on the torus and extend them for more general classes of perturbations. Additionally, we construct examples of low order perturbations that destroy the global hypoellipticity, in the presence of diophantine phenomena

Cite this article

Fernando de Ávila Silva, Alexandre Kirilov, Perturbations of globally hypoelliptic operators on closed manifolds. J. Spectr. Theory 9 (2019), no. 3, pp. 825–855

DOI 10.4171/JST/264