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 ∞ in any half-space of ℝ2n.
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Communicated by John J. Benedetto
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Janssen, A.J.E.M. Proof of a conjecture on the supports of Wigner distributions. The Journal of Fourier Analysis and Applications 4, 723–726 (1998). https://doi.org/10.1007/BF02479675
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DOI: https://doi.org/10.1007/BF02479675