"On Cohen's class distributions"
Skrettingland, EirikWe show that distributions in Cohen's class are intrinsically linked with quantum harmonic analysis. Namely, we give a characterization of Cohen's class as convolutions with a fixed operator. Hence many properties of the Cohen's class distribution may be precisely described as properties of the corresponding operator. We apply the theory of convolutions of operators to deduce results on Cohen's class distributions and study when these are positive and have the correct total energy property. We show that these Cohen class distributions are all given as linear combinations of the spectrogram. A further consequence of our approach is a weak uncertainty principle for Cohen's class distributions that extends uncertainty principles for the spectrogram and Wigner distribution.