Capoferri, Matteo;
Vassiliev, Dmitri;
(2022)
Invariant subspaces of elliptic systems II: Spectral theory.
Journal of Spectral Theory
, 12
(1)
pp. 301-338.
10.4171/jst/402.
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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 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.
| Type: | Article |
|---|---|
| Title: | Invariant subspaces of elliptic systems II: Spectral theory |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4171/jst/402 |
| Publisher version: | http://dx.doi.org/10.4171/JST/402 |
| 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, hyperbolic systems, invariant subspaces, spectral asymptotics, 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/10146572 |
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