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Elliptic, parabolic and hyperbolic operators. Laplace, Laplace-Beltrami, Schrödinger, Dirac. Exterior derivative and Lie derivative operators.

8 votes

Symbol of pseudodiff operator

There are several global approaches to pseudo-diffops. All of them seem to need some additional geometric objects, a connection. So suppose that you want to have $\Psi$DO's on some vector bundle $E \l …
Stefan Waldmann's user avatar
3 votes
Accepted

Horizontal lift of differential operator

This is a sort of standard construction you can find in several places. I don't know where this was done first though... OK: first you can extend your horizontal lift from vector fields to all (symm …
Stefan Waldmann's user avatar
16 votes
Accepted

Hodge decomposition of smooth n-forms: is it an isomorphism of topological vector spaces?

Maybe an even more elementary argument than the one of Tobias: The continuity of all involved operators is easy: simply all differential operators with smooth coefficients between sections of vector b …
Stefan Waldmann's user avatar