Geodesic
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 Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 225-232

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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 $27\leq d1450$.
Keywords: Delsarte method, infinite-dimensional linear programming, Gegenbauer polynomials, kissing numbers. 
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     author = {N. A. Kuklin},
     title = {The form of an extremal function in the {Delsarte} problem of finding an upper bound for the kissing number in the three-dimensional space},
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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 Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 225-232. http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a21/