TOPOLOGICAL OBSTRUCTIONS TO THE DIAGONALISATION OF PSEUDODIFFERENTIAL SYSTEMS
Journal article, 2022
Given a matrix pseudodifferential operator on a smooth manifold, one may be interested in diagonalising it by choosing eigenvectors of its prin-cipal 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 iden-tify global and local topological obstructions to diagonalisation and examine physically meaningful examples demonstrating that all possible scenarios can occur.
Author
Matteo Capoferri
Cardiff University
Grigori Rozenblioum
Chalmers, Mathematical Sciences
Euler International Mathematical Institute
Sirius University of Science and Technology
Nikolai Saveliev
University of Miami
Dmitri Vassiliev
University College London (UCL)
Proceedings of the American Mathematical Society, Series B
23301511 (eISSN)
Vol. 9 43 472-486Subject Categories
Computational Mathematics
Geometry
Mathematical Analysis
DOI
10.1090/bproc/147