Geodesic
Delsarte method in the problem on kissing numbers in high-dimensional spaces
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 224-239 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 the 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.
Keywords: Delsarte method, infinite-dimensional linear programming, Gegenbauer polynomials, kissing numbers. 
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N. A. Kuklin. Delsarte method in the problem on kissing numbers in high-dimensional spaces. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 224-239. http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a19/

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