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arXiv · 2203.16957

Topological obstructions to the diagonalisation of pseudodifferential systems

Matteo Capoferri·Grigori Rozenblum·Nikolai Saveliev·Dmitri Vassiliev
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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.

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Matteo Capoferri, Grigori Rozenblum, Nikolai Saveliev, Dmitri Vassiliev. 2022-03-31. Topological obstructions to the diagonalisation of pseudodifferential systems. https://doi.org/10.1090/bproc/147

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