Capoferri, Matteo  ORCID: https://orcid.org/0000-0001-6226-1407 and Vassiliev, Dmitri
2022.
Invariant subspaces of elliptic systems I: Pseudodifferential projections.
Journal of Functional Analysis
282
(8)
, 109402.
10.1016/j.jfa.2022.109402
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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 into invariant subspaces under the action of A modulo . 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.
| Item Type: | Article |
|---|---|
| Date Type: | Publication |
| Status: | Published |
| Schools: | Schools > Mathematics |
| Publisher: | Elsevier |
| ISSN: | 0022-1236 |
| Funders: | Leverhulme Trust |
| Date of First Compliant Deposit: | 9 February 2022 |
| Date of Acceptance: | 13 January 2022 |
| Last Modified: | 14 Nov 2024 10:15 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/147338 |
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