Capoferri, Matteo;
Rozenblum, Grigori;
Saveliev, Nikolai;
Vassiliev, Dmitri;
(2022)
Topological obstructions to the diagonalisation of pseudodifferential systems.
arXiv: Ithaca, NY, USA.
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Abstract
Given a matrix pseudodifferential operator on a smooth manifold, one may be interested in diagonalising it by choosing eigenvectors of its principal symbol in a smooth manner. We show that diagonalisation is not always possible, on the whole cotangent bundle or even in a single fibre. We identify global and local topological obstructions to diagonalisation and examine physically meaningful examples demonstrating that all possible scenarios can occur.
| Type: | Working / discussion paper |
|---|---|
| Title: | Topological obstructions to the diagonalisation of pseudodifferential systems |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.48550/arXiv.2203.16957 |
| Publisher version: | https://doi.org/10.48550/arXiv.2203.16957 |
| Language: | English |
| Additional information: | Copyright © The Author 2022. This work is licensed under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/). |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS 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 |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10167540 |
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