Linear perturbations of the Wigner distribution and the Cohen class
Copyright policy )Linear perturbations of the Wigner distribution and the Cohen class
The Wigner distribution is a milestone of Time–frequency Analysis. In order to cope with its drawbacks while preserving the desirable features that made it so popular, several kinds of modifications have been proposed. This contribution fits into this perspective. We introduce a family of phase-space representations of Wigner type associated with invertible matrices and explore their general properties. As a main result, we provide a characterization for the Cohen’s class [L. Cohen, Generalized phase-space distribution functions, J. Math. Phys. 7 (1996) 781–786; Time–frequency Analysis (Prentice Hall, New Jersey, 1995)]. This feature suggests to interpret this family of representations as linear perturbations of the Wigner distribution. We show which of its properties survive under linear perturbations and which ones are truly distinctive of its central role.
- Polytechnic University of Turin Italy
- University of Turin Italy
Wiener amalgam spaces, Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics, time-frequency analysis, Cohen's class; Modulation spaces; Time-frequency analysis; Wiener amalgam spaces; Wigner distribution, Operations with distributions and generalized functions, Functional Analysis (math.FA), Mathematics - Functional Analysis, 42A38, 42B35, 46F10, 46F12, 81S30, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Mathematics - Classical Analysis and ODEs, Wigner distribution, Cohen's class, Cohen's class; modulation spaces; Time-frequency analysis; Wiener amalgam spaces; Wigner distribution, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Integral transforms in distribution spaces, Function spaces arising in harmonic analysis, modulation spaces
Wiener amalgam spaces, Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics, time-frequency analysis, Cohen's class; Modulation spaces; Time-frequency analysis; Wiener amalgam spaces; Wigner distribution, Operations with distributions and generalized functions, Functional Analysis (math.FA), Mathematics - Functional Analysis, 42A38, 42B35, 46F10, 46F12, 81S30, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Mathematics - Classical Analysis and ODEs, Wigner distribution, Cohen's class, Cohen's class; modulation spaces; Time-frequency analysis; Wiener amalgam spaces; Wigner distribution, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Integral transforms in distribution spaces, Function spaces arising in harmonic analysis, modulation spaces
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