Modulation space

Summary

A modulation space $M^{p,q}(\R^d)$ is a space of tempered distributions defined by the size of their short-time Fourier transform. The exponent $p$ measures integrability in the time variable and $q$ in the frequency variable. Modulation spaces are the natural function spaces of time–frequency analysis. They are used to study pseudo-differential operators, Gabor expansions and dispersive equations.