A Note on Hudson’s Theorem about Functions with Nonnegative Wigner Distributions

DOI10.1137/0515014zbMath0541.46035OpenAlexW2039667651MaRDI QIDQ3327166

Augustus J. E. M. Janssen

Publication date: 1984

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0515014

zbMATH Keywords

Gelfand-Shilov spaceBargmann transformGabor function

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Analysis on other specific Lie groups (43A80) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

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A transformation property of the Wigner distribution under Hamiltonian symplectomorphisms ⋮ Linear perturbations of the Wigner distribution and the Cohen class ⋮ Orbital angular momentum in phase space ⋮ The wave front set of the Wigner distribution and instantaneous frequency ⋮ Zeros of the Wigner distribution and the short-time Fourier transform ⋮ Quantum forced oscillator via Wigner transform ⋮ The Moyal representation of quantum mechanics and special function theory ⋮ Quantum Harmonic Analysis of the Density Matrix ⋮ Linear Perturbations of the Wigner Transform and the Weyl Quantization ⋮ Wigner quasi-probability densities and characterization of the Gaussian distribution. ⋮ What information about a wave function is given by ``measuring it with the help of the tomographic method of recovering the Wigner distribution? ⋮ Wigner functions on non-standard symplectic vector spaces ⋮ Bilinear phase-plane distribution functions and positivity

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