The differentiation operator is an isomorphism between Sobolev spaces, and certain time-frequency localization operators are isomorphisms between modulation spaces. On an abstract level, weighted coorbit spaces with respect to a localized frame are isomorphic via frame multipliers. I will try to show some (new) tricks about spectral invariance that are necessary to prove such results.
This is joint work in progress with Peter Balazs, Austrian Academy of Sciences.
https://univienna.zoom.us/j/67922750549?pwd=Ulh5L1QxNFhBOC9PUjlVdG9hc0tmUT09