Localization of multidimensional Wigner distributions

Elliott H. Lieb; Yaron Ostrover

doi:10.1063/1.3486068

Localization of multidimensional Wigner distributions

Elliott H. Lieb, Yaron Ostrover

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

A well known result of P. Flandrin states that a Gaussian uniquely maximizes the integral of the Wigner distribution over every centered disk in the phase plane. While there is no difficulty in generalizing this result to higher-dimensional polydisks, the generalization to balls is less obvious. In this note we provide such a generalization.

Original language	English (US)
Article number	102101
Journal	Journal of Mathematical Physics
Volume	51
Issue number	10
DOIs	https://doi.org/10.1063/1.3486068
State	Published - Oct 2010

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.3486068

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title = "Localization of multidimensional Wigner distributions",

abstract = "A well known result of P. Flandrin states that a Gaussian uniquely maximizes the integral of the Wigner distribution over every centered disk in the phase plane. While there is no difficulty in generalizing this result to higher-dimensional polydisks, the generalization to balls is less obvious. In this note we provide such a generalization.",

author = "Lieb, \{Elliott H.\} and Yaron Ostrover",

note = "Funding Information: We thank P. Flandrin, A. J. E. M. Janssen, and F. Luef for helpful discussions. This work was partially supported by the U.S National Science Foundation under Grant Nos. PHY-0965859 (E.H.L.) and DMS-0635607 (Y.O.).",

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PY - 2010/10

Y1 - 2010/10

N2 - A well known result of P. Flandrin states that a Gaussian uniquely maximizes the integral of the Wigner distribution over every centered disk in the phase plane. While there is no difficulty in generalizing this result to higher-dimensional polydisks, the generalization to balls is less obvious. In this note we provide such a generalization.

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Localization of multidimensional Wigner distributions

Abstract

All Science Journal Classification (ASJC) codes

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