Coorbit space theory is an abstract approach to function spaces and their atomic decompositions. The original theory developed by Feichtinger and Gröchenig in the late 1980ies heavily uses integrable representations of locally compact groups. Their theory covers, in particular, homogeneous Besov-Lizorkin-Triebel spaces, modulation spaces, Bergman spaces and the recent shearlet spaces. However, ...

Abstract We give a new class of equivalent norms for modulation spaces by replacing the window short-time Fourier transform Hilbert–Schmidt operator. The main result is applied to Cohen’s time-frequency distributions, Weyl operators and localization operators. In particular, any positive distribution with Schwartz kernel can be used an norm spaces. also obtain description as Wiener amalgam oper...

It is proved that modulation in time and space of periodic wave trains, the defocussing nonlinear Schr\"odinger equation, can be approximated by solutions Whitham equations, hyperbolic case, on a natural scale. The error estimates are based existence, uniqueness, energy arguments, Sobolev spaces real line. An essential part proof inclusion higher-order corrections to theory, concomitant estimat...