Equivalent Norms for Modulation Spaces from Positive Cohen’s Class Distributions

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 operator must satisfy nuclearity condition these results hold, we investigate this in detail.