Invariant subspaces of elliptic systems II: Spectral theory

Matteo Capoferri, Dmitri Vassiliev

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


Consider an elliptic self-adjoint pseudodifferential operator A acting on m-columns of half-densities on a closed manifold M, whose principal symbol is assumed to have simple eigenvalues. We show that the spectrum of A decomposes, up to an error with superpolynomial decay, into m distinct series, each associated with one of the eigenvalues of the principal symbol of A. These spectral results are then applied to the study of propagation of singularities in hyperbolic systems. The key technical ingredient is the use of the carefully devised pseudodifferential projections introduced in the first part of this work, which decompose L2.M / into almost-orthogonal almost-invariant subspaces under the action of both A and the hyperbolic evolution.

Original languageEnglish
Pages (from-to)301-338
Number of pages38
JournalJournal of Spectral Theory
Issue number1
Publication statusPublished - 24 Mar 2022


  • elliptic systems
  • hyperbolic systems
  • invariant subspaces
  • pseudodifferential operators on manifolds
  • Pseudodifferential projections
  • spectral asymptotics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Geometry and Topology


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