Turan Extremum Problem for Periodic Function with Small Support
Abstract
We consider an extremum problem posed by Turan. The aim of this problem is to find a maximum mean value of 1-periodic continuous even function such that sum of Fourier coefficient modules for this function is equal to 1 and support of this function lies in [-h,h], 0<h 1/2. We show that this extremum problem for rational h=p/q is equivalent two finite-dimensional linear programming problems. Here there are exact results for rational h=2/q, h=p/(2p+1), h=3/q, and asymptotic equalities.
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