Proof of a conjecture on the supports of Wigner distributions

DOI10.1007/BF02479675zbMath0924.42009WikidataQ123221349 ScholiaQ123221349MaRDI QIDQ1282025

Augustus J. E. M. Janssen

Publication date: 8 November 1999

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/59590

zbMATH Keywords

uncertainty principleambiguity functionWigner distribution

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Signal theory (characterization, reconstruction, filtering, etc.) (94A12)

Related Items (23)

Wigner Representations Associated with Linear Transformations of the Time-Frequency Plane ⋮ Uncertainty principle, positivity and \(L^{p}\)-boundedness for generalized spectrograms ⋮ Windowed-Wigner representations in the Cohen class and uncertainty principles ⋮ Weighted integrals of Wigner representations ⋮ Invertibility of positive Toeplitz operators and associated uncertainty principle ⋮ A stable quantum Darmois-Skitovich theorem ⋮ The wave front set of the Wigner distribution and instantaneous frequency ⋮ Time-frequency partitions and characterizations of modulation spaces with localization operators ⋮ Uncertainty principle for Weyl transform and Fourier–Wigner transform ⋮ Cohen class of time-frequency representations and operators: boundedness and uncertainty principles ⋮ A refinement of the Robertson-Schrödinger uncertainty principle and a Hirschman-Shannon inequality for Wigner distributions ⋮ Time-frequency analysis of localization operators. ⋮ A Wiener Tauberian theorem for operators and functions ⋮ Localization operators and an uncertainty principle for the discrete short time Fourier transform ⋮ Supports of representations in the Cohen class ⋮ Some Localization Properties of the L^p Continuous Wavelet Transform ⋮ Time–frequency concentration of the windowed Hankel transform ⋮ Benedicks’ theorem for the Heisenberg group ⋮ On uncertainty principles in the finite dimensional setting ⋮ Time-frequency representations of Wigner type and pseudo-differential operators ⋮ Annihilating sets for the short time Fourier transform ⋮ On Gabor g-frames and Fourier series of operators ⋮ Quantum harmonic analysis on lattices and Gabor multipliers

Cites Work

• Unnamed Item
• On Fourier transforms of functions supported on sets of finite Lebesgue measure
• The uncertainty principle: A mathematical survey
• Regularity and unitarity of bilinear time-frequency signal representations
• Harmonic Analysis in Phase Space. (AM-122)

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