Capoferri, Matteo;
Vassiliev, Dmitri;
(2022)
Invariant subspaces of elliptic systems I: pseudodifferential projections.
Journal of Functional Analysis
, Article 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 L 2 (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.
| Type: | Article |
|---|---|
| Title: | Invariant subspaces of elliptic systems I: pseudodifferential projections |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.jfa.2022.109402 |
| Publisher version: | https://doi.org/10.1016/j.jfa.2022.109402 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Pseudodifferential projections, elliptic systems, invariant subspaces, pseudodifferential operators on manifolds |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10142906 |
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