ON AN EXTREMAL PROBLEM FOR POLYNOMIALS WITH FIXED MEAN VALUE

Alexander G. Babenko     (Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences; Institute of Mathematics and Computer Science of the Ural Federal University, Ekaterinburg, Russian Federation)

Abstract


Let \(T_n^+\) be the set of nonnegative trigonometric polynomials \(\tau_n\) of degree \(n\) that are strictly positive at zero. For \(0\le\alpha\le2\pi/(n+2),\) we find the minimum of the mean value of polynomial \((\cos\alpha-\cos{x})\tau_n(x)/\tau_n(0)\) over \(\tau_n\in T_n^+\) on the period \([-\pi,\pi).\)


Keywords


Trigonometric polynomials, Extremal problem

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References


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DOI: http://dx.doi.org/10.15826/umj.2016.1.001

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