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On the extremal problem on the minimum of the free term of a nonnegative trigonometric polynomial

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Abstract

We solve a new extremal problem on the minimum of the free term of a nonnegative even trigonometric polynomial with the following conditions on its coefficients: all coefficients except for the free term are greater than or equal to 1 and the sum of all coefficients except for the free term is equal to a specified value. As a result, Fejér’s known result is improved.

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References

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Authors and Affiliations

  1. Ivanovo State University, ul. Ermaka 39, Ivanovo, 153025, Russia

    A. S. Belov

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  1. A. S. Belov
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Correspondence to A. S. Belov.

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Original Russian Text © A.S. Belov, 2011, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2011, Vol. 17, No. 3.

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Belov, A.S. On the extremal problem on the minimum of the free term of a nonnegative trigonometric polynomial. Proc. Steklov Inst. Math. 277 (Suppl 1), 55–72 (2012). https://doi.org/10.1134/S0081543812050070

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  • DOI: https://doi.org/10.1134/S0081543812050070

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