``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
BOGGIATTO, Paolo;CARYPIS, EVANTHIA;OLIARO, Alessandro
2012-01-01
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.File in questo prodotto:
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