Windowed-Wigner Representations, Interferences and Operators

2010 Mathematics Subject Classification: 42B10, 47A07, 35S05.

“Windowed-Wigner” representations, denoted by Wig and Wig_ , were introduced in [2] in connection with uncertainty principles and interferences problems. In this paper we present a more precise analysis of their behavior obtaining an estimate of the L2-norm of interferences of couples of “model” signals. We further define a suitable functional framework for the associated operators and show that they form a class of pseudodifferential operators which define a natural “path” between the multiplication, Weyl and Fourier multipliers operators.