RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Trudy Inst. Mat. i Mekh. UrO RAN, 2011, Volume 17, Number 3, Pages 225–232 (Mi timm734)  

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.

Full text: PDF file (173 kB)
References: PDF file   HTML file
UDC: 517.518.86+519.147
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

Citation in format AMSBIB
\Bibitem{Kuk11}
\by N.~A.~Kuklin
\paper The form of an extremal function in the Delsarte problem of finding an upper bound for the kissing number in the three-dimensional space
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2011
\vol 17
\issue 3
\pages 225--232
\mathnet{http://mi.mathnet.ru/timm734}
\elib{http://elibrary.ru/item.asp?id=17870134}


Linking options:
  • http://mi.mathnet.ru/eng/timm734
  • http://mi.mathnet.ru/eng/timm/v17/i3/p225

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. A. Kuklin, “Delsarte method in the problem on kissing numbers in high-dimensional spaces”, Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 108–123  mathnet  crossref  isi  elib
    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  mathnet  crossref  mathscinet  isi  elib
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
    Number of views:
    This page:245
    Full text:90
    References:41
    First page:5

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020