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 Trudy Inst. Mat. i Mekh. UrO RAN, 2011, Volume 17, Number 3, Pages 225–232 (Mi timm734)

The form of an extremal function in the Delsarte problem of finding an upper bound for the kissing number in the three-dimensional space

N. A. Kuklin

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: We consider an extremal problem for continuous functions that are nonpositive on a closed interval and can be represented by series in Legendre polynomials with nonnegative coefficients. This problem arises from the Delsarte method of finding an upper bound for the kissing number in the three-dimensional Euclidean space. We prove that all extremal functions in this problem are algebraic polynomials and the degree $d$ of each polynomial satisfies the inequalities $27\leq d<1450$.

Keywords: Delsarte method, infinite-dimensional linear programming, Gegenbauer polynomials, kissing numbers.

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Citation: N. A. Kuklin, “The form of an extremal function in the Delsarte problem of finding an upper bound for the kissing number in the three-dimensional space”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 3, 2011, 225–232

Citation in format AMSBIB
\Bibitem{Kuk11} \by N.~A.~Kuklin \paper The form of an extremal function in the Delsarte problem of finding an upper bound for the kissing number in the three-dimensional space \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2011 \vol 17 \issue 3 \pages 225--232 \mathnet{http://mi.mathnet.ru/timm734} \elib{http://elibrary.ru/item.asp?id=17870134} 

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This publication is cited in the following articles:
1. N. A. Kuklin, “Delsarte method in the problem on kissing numbers in high-dimensional spaces”, Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 108–123
2. N. A. Kuklin, “The extremal function in the Delsarte problem of finding an upper bound for the kissing number in the three-dimensional space”, Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 99–111
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