Uncertainty principle, positivity and L-boundedness for generalized spectrograms

In this paper we are concerned with the properties of positivity, uncertainty principle and continuity in Lp spaces of a generalized spectrogram. In particular we study the connections of a generalized spectrogram, as a subclass of the Cohen class, with the Rihaczek and the Wigner representations. We also consider the behavior of the generalized spectrogram with respect to the positivity and the Lp boundedness of the corresponding localization operators. © 2007 Elsevier Inc. All rights reserved.