Topological obstructions to the diagonalisation of pseudodifferential systems

Capoferri, Matteo; Rozenblum, Grigori; Saveliev, Nikolai; Vassiliev, Dmitri

doi:10.1090/bproc/147

Topological obstructions to the diagonalisation of pseudodifferential systems
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by Matteo Capoferri, Grigori Rozenblum, Nikolai Saveliev and Dmitri Vassiliev HTML | PDF

Proc. Amer. Math. Soc. Ser. B 9 (2022), 472-486

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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