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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2011, Volume 17, Number 3, Pages 225–232
(Mi timm734)
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This article is cited in 2 scientific papers (total in 2 papers)
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.
Received: 01.07.2011
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
Linking options:
https://www.mathnet.ru/eng/timm734 https://www.mathnet.ru/eng/timm/v17/i3/p225
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