Determinacy for Measures
نویسنده
چکیده
For a given finite positive measure we determine the minimal information that is needed from its Fourier transform to determine the measure completely. In particular, we show that if the support of a measure doesn’t contain a sequence of Beurling-Malliavin interior density d > 0 then the interval of determinacy for this measure must be of length larger than πd. As a consequence, we provide a sharp lower estimate of the rate of oscillation of high pass signals in terms of their spectral gap. This gives a considerably shorter and more informative proof of the estimate previously obtained by A. Eremenko and D. Novikov.
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