Topological obstructions to the diagonalisation of pseudodifferential systems

Matteo Capoferri, Grigori Rozenblum, Nikolai Saveliev, Dmitri Vassiliev

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
22 Downloads (Pure)


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
Pages (from-to)472-486
Number of pages15
JournalProceedings of the American Mathematical Society: Series B
Issue number43
Publication statusPublished - 27 Dec 2022


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

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Geometry and Topology
  • Algebra and Number Theory


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