Topological obstructions to the diagonalisation of pseudodifferential systems

Matteo Capoferri, Grigori Rozenblum, Nikolai Saveliev, Dmitri Vassiliev

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
JournalProceedings of the American Mathematical Society: Series B
DOIs
Publication statusAccepted/In press - 19 Oct 2022

Keywords

  • math.AP
  • math-ph
  • math.MP
  • primary 58J40, secondary 35G35, 35J46, 35J47, 35J48

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