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Delsarte method in the problem on kissing numbers in high-dimensional spaces

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Abstract

We consider extremal problems for continuous functions that are nonpositive on a closed interval and can be represented as series in Gegenbauer polynomials with nonnegative coefficients. These problems arise from the Delsarte method of finding an upper bound for the kissing number in a Euclidean space. We develop a general method for solving such problems. Using this method, we reproduce results of previous authors and find a solution in the following 11 new dimensions: 147, 157, 158, 159, 160, 162, 163, 164, 165, 167, and 173. The arising extremal polynomials are of a new type.

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Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Ural Federal University, pr. Lenina 51, Yekaterinburg, 620000, Russia

    N. A. Kuklin

  2. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia

    N. A. Kuklin

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  1. N. A. Kuklin
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Correspondence to N. A. Kuklin.

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Original Russian Text © N.A. Kuklin, 2012, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2012, Vol. 18, No. 4.

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Kuklin, N.A. Delsarte method in the problem on kissing numbers in high-dimensional spaces. Proc. Steklov Inst. Math. 284 (Suppl 1), 108–123 (2014). https://doi.org/10.1134/S0081543814020102

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