Windowed-Wigner'' representations, denoted by $\Wig_\psi$ and $\Wig_\psi^*$, were introduced in \cite{BogCarOli2012} 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 $L^2$-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 pseudo-differential operators which define a natural path'' between the multiplication, Weyl and Fourier multipliers operators.

### Windowed-Wigner Representations, Interferences and Operators

#### Abstract

Windowed-Wigner'' representations, denoted by $\Wig_\psi$ and $\Wig_\psi^*$, were introduced in \cite{BogCarOli2012} 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 $L^2$-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 pseudo-differential operators which define a natural path'' between the multiplication, Weyl and Fourier multipliers operators.
##### Scheda breve Scheda completa Scheda completa (DC)
2012
Conference on Partial Dierential Equations and Applications
Sofia, Bulgaria
14-17 settembre 2011
21
97
112
Wigner type representations; Pseudodifferential operators; Interference
P. Boggiatto; E. Carypis; A. Oliaro
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/131134