Multilinear tau-Wigner transform

Abstract

In this work, we introduce a tau-dependent multilinear Wigner transform W-tau, tau is an element of [0, 1](d). It also includes various types of multilinear time-frequency representations, among the others the classical multilinear Wigner and Rihaczek representations and some properties of multilinear tau-Wigner transform. We then prove the boundedness properties of multilinear tau-Wigner transform both on products of Lebesgue spaces and on modified version of modulation spaces.