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.
|Journal||Proceedings of the American Mathematical Society: Series B|
|Publication status||Accepted/In press - 19 Oct 2022|
- primary 58J40, secondary 35G35, 35J46, 35J47, 35J48