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We consider the Turan n-dimensional extremum problem of finding the value of An(hBn) which is equal to the maximum zero Fourier coefficient $$\widehat f_0$$ of periodic functions f supported in the Euclidean ball hBn of radius h, having nonnegative Fourier coefficients, and satisfying the condition f(0)= 1. This problem originates from applications to number theory. The case of A1([−h,h...
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