We study the set N Ω of zeros of the Fourier transform of the characteristic function of a centrally symmetric convex domain Ω in the plane and the functional κ(Ω) = dist(0,N Ω). We prove that, if Ω is not a polygon, then N Ω is the countable union of disjoint analytic curves. We also show that, among centrally symmetric convex domains of a fixed area, there exists a domain where the functional κ attains the maximum. Bibliography: 4 titles.
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Translated from Problemy Matematicheskogo Analiza 75, April 2014, pp. 81–92.
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Ryadovkin, K., Filonov, N. The Set of Zeros of the Fourier Transform of the Characteristic Function of a Symmetric Convex Domain. J Math Sci 198, 747–760 (2014). https://doi.org/10.1007/s10958-014-1823-1
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DOI: https://doi.org/10.1007/s10958-014-1823-1