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Algebra i Analiz, 2010, Volume 22, Issue 5, Pages 131–139 (Mi aa1207)  

This article is cited in 3 scientific papers (total in 3 papers)

Research Papers

Extremal properties of spherical semidesigns

N. O. Kotelina, A. B. Pevnyĭ

Syktyvkar State University, Faculty of Mathematics, Syktyvkar, Russia

Abstract: For every even $t\geq2$ and every set of vectors $\Phi=\{\varphi_1,…,\varphi_m\}$ on the sphere $S^{n-1}$, the notion of the $t$-potential $P_t(\Phi)=\sum^m_{i,j=1}[\langle\varphi_i,\varphi_j\rangle]^t$ is introduced. It is proved that the minimum value of the $t$-potential is attained at the spherical semidesigns of order $t$ and only at them. The first result of this type was obtained by B. B. Venkov. The result is extended to the case of sets $\Phi$ that do not lie on the sphere $S^{n-1}$. For the V. A. Yudin potentials $U_k(\Phi)$, $k=2,4,…,t$, it is shown that they attain the minimal value at the spherical semidesigns of order $t$ and only at them.

Keywords: spherical designs, spherical semidesigns.

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English version:
St. Petersburg Mathematical Journal, 2011, 22:5, 795–801

Bibliographic databases:

Document Type: Article
Received: 04.08.2009

Citation: N. O. Kotelina, A. B. Pevnyǐ, “Extremal properties of spherical semidesigns”, Algebra i Analiz, 22:5 (2010), 131–139; St. Petersburg Math. J., 22:5 (2011), 795–801

Citation in format AMSBIB
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\paper Extremal properties of spherical semidesigns
\jour Algebra i Analiz
\yr 2010
\vol 22
\issue 5
\pages 131--139
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2828829}
\zmath{https://zbmath.org/?q=an:1231.05050}
\transl
\jour St. Petersburg Math. J.
\yr 2011
\vol 22
\issue 5
\pages 795--801
\crossref{https://doi.org/10.1090/S1061-0022-2011-01168-9}
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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. Nozaki H., Shinohara M., “A geometrical characterization of strongly regular graphs”, Linear Algebra Appl., 437:10 (2012), 2587–2600  crossref  mathscinet  zmath  isi  elib  scopus
    2. Pevnyi A.B., Kotelina N.O., “Kompleksnye sfericheskie poludizainy”, Vestnik syktyvkarskogo universiteta. seriya 1: matematika. mekhanika. informatika, 2013, no. 17, 35–43  elib
    3. N. O. Kotelina, A. B. Pevnyi, “Sidelnikov inequality”, St. Petersburg Math. J., 26:2 (2015), 351–356  mathnet  crossref  mathscinet  isi  elib
  • Алгебра и анализ St. Petersburg Mathematical Journal
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