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- W3131569129 abstract "We review several properties of integrals of the Wigner distribution on subsets of the phase space. Along our way, we provide a theoretical proof of the invalidity of Flandrin's conjecture, a fact already proven via numerical arguments in our joint paper [MR4054880] with B.Delourme and T.Duyckaerts. We use also the J.G.Wood and A.J.Bracken paper [MR2131219], for which we offer a mathematical perspective. We review thoroughly the case of subsets of the plane whose boundary is a conic curve and show that Mehler's formula can be helpful in the analysis of these cases, including for the higher dimensional case investigated in the paper [MR2761287] by E.Lieb and Y.Ostrover. Using the Feichtinger algebra, we show that, generically in the Baire sense, the Wigner distribution of a pulse in $L^2(mathbb R^n)$ does not belong to $L^1(mathbb R^{2n})$, providing as a byproduct a large class of examples of subsets of the phase space $mathbb R^{2n}$ on which the integral of the Wigner distribution is infinite. We study as well the case of convex polygons of the plane, with a rather weak estimate depending on the number of vertices, but independent of the area of the polygon." @default.
- W3131569129 created "2021-03-01" @default.
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- W3131569129 date "2022-09-07" @default.
- W3131569129 modified "2023-09-23" @default.
- W3131569129 title "INTEGRATING THE WIGNER DISTRIBUTION ON SUBSETS OF THE PHASE SPACE, A SURVEY" @default.
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