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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2012, Volume 18, Number 4, Pages 224–239 (Mi timm881)  
This article is cited in 3 scientific papers (total in 3 papers)

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
Full-text PDF (248 kB) Citations (3)
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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.
Received: 29.02.2012
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, Volume 284, Issue 1, Pages 108–123
DOI: https://doi.org/10.1134/S0081543814020102
Bibliographic databases:
Document Type: Article
UDC: 517.518.86+519.147
Language: Russian
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
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\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{https://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}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84898753222}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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