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We determine a class of real valued, integrable functions f (x) and corresponding functions Mf (x) such that f (x) Mf (x) for all x, the Fourier transform Mf (t) is zero when | t | 1, and the value of Mf (0) is minimized. Several applications of these functions to number theory and analysis are given.
Graham et al. (Thu,) studied this question.
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