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 Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 4, Pages 224–239 (Mi timm881)

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

N. A. Kuklinab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University

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 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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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, 284, suppl. 1, 108–123

Bibliographic databases:

UDC: 517.518.86+519.147

Citation: N. A. Kuklin, “Delsarte method in the problem on kissing numbers in high-dimensional spaces”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 4, 2012, 224–239; Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 108–123

Citation in format AMSBIB
\Bibitem{Kuk12} \by N.~A.~Kuklin \paper Delsarte method in the problem on kissing numbers in high-dimensional spaces \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2012 \vol 18 \issue 4 \pages 224--239 \mathnet{http://mi.mathnet.ru/timm881} \elib{http://elibrary.ru/item.asp?id=18126484} \transl \jour Proc. Steklov Inst. Math. (Suppl.) \yr 2014 \vol 284 \issue , suppl. 1 \pages 108--123 \crossref{https://doi.org/10.1134/S0081543814020102} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000334277400010} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84898753222} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. V. V. Arestov, M. A. Filatova, “On the approximation of the differentiation operator by linear bounded operators on the class of twice differentiable functions in the space $L_2(0,\infty)$”, Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 24–40
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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