Almost Diagonalization of ΨDO’s Over Various Generalized Function Spaces

Inductive and projective type sequence spaces of sub- and super-exponential growth, and the corresponding inductive and projective limits of modulation spaces are considered as a framework for almost diagonalization of pseudo-differential operators. Moreover, recent results of the first author and B. Prangoski related to the almost diagonalization of pseudo-differential operators in the context of Hormander metrics are reviewed. 2010 Mathematics Subject Classification. 47G30, 46F05, 42C15, 58J40.