Proof of a conjecture on the supports of Wigner distributions

A.J.E.M. Janssen

doi:10.1007/BF02479675

Proof of a conjecture on the supports of Wigner distributions

A.J.E.M. Janssen

Control Systems

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Abstract

In this note we prove that the Wigner distribution of an f ¿ L²(Rⁿ) cannot be supported by a set of finite measure in R²ⁿ unless f = 0. We prove a corresponding statement for cross-ambiguity functions. As a strengthening of the conjecture we show that for an f ¿ L²(Rⁿ) its Wigner distribution has a support of measure 0 or 8 in any half-space of R²ⁿ.

Original language	English
Pages (from-to)	723-726
Number of pages	4
Journal	Journal of Fourier Analysis and Applications
Volume	4
Issue number	6
DOIs	https://doi.org/10.1007/BF02479675
Publication status	Published - 1998

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title = "Proof of a conjecture on the supports of Wigner distributions",

abstract = "In this note we prove that the Wigner distribution of an f ¿ L2(Rn) cannot be supported by a set of finite measure in R2n unless f = 0. We prove a corresponding statement for cross-ambiguity functions. As a strengthening of the conjecture we show that for an f ¿ L2(Rn) its Wigner distribution has a support of measure 0 or 8 in any half-space of R2n.",

author = "A.J.E.M. Janssen",

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T1 - Proof of a conjecture on the supports of Wigner distributions

AU - Janssen, A.J.E.M.

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Y1 - 1998

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AB - In this note we prove that the Wigner distribution of an f ¿ L2(Rn) cannot be supported by a set of finite measure in R2n unless f = 0. We prove a corresponding statement for cross-ambiguity functions. As a strengthening of the conjecture we show that for an f ¿ L2(Rn) its Wigner distribution has a support of measure 0 or 8 in any half-space of R2n.

U2 - 10.1007/BF02479675

DO - 10.1007/BF02479675

M3 - Article

SN - 1069-5869

VL - 4

SP - 723

EP - 726

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 6

ER -

Proof of a conjecture on the supports of Wigner distributions

Abstract

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