Invariant subspaces of elliptic systems I: Pseudodifferential projections

Matteo Capoferri, Dmitri Vassiliev*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

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 existence and uniqueness of m orthonormal pseudodifferential projections commuting with the operator A and provide an algorithm for the computation of their full symbols, as well as explicit closed formulae for their subprincipal symbols. Pseudodifferential projections yield a decomposition of L2(M) into invariant subspaces under the action of A modulo C(M). Furthermore, they allow us to decompose A into m distinct sign definite pseudodifferential operators. Finally, we represent the modulus and the Heaviside function of the operator A in terms of pseudodifferential projections and discuss physically meaningful examples.

Original languageEnglish
Article number109402
JournalJournal of Functional Analysis
Volume282
Issue number8
Early online date21 Jan 2022
DOIs
Publication statusPublished - 15 Apr 2022

Keywords

  • Elliptic systems
  • Invariant subspaces
  • Pseudodifferential operators on manifolds
  • Pseudodifferential projections

ASJC Scopus subject areas

  • Analysis

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