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Izv. RAN. Ser. Mat., 2005, Volume 69, Issue 5, Pages 205–224 (Mi izv661)  

This article is cited in 2 scientific papers (total in 2 papers)

Distribution of the points of a design on the sphere

V. A. Yudin

Moscow Power Engineering Institute (Technical University)

Abstract: We determine the size of spherical caps with centres at the points of a design that cover the whole sphere in Euclidean space with a given multiplicity. By projecting $q$-designs on one-dimensional subspaces, we obtain the nodes of a Chebyshev-type quadrature formula of the same precision $q$. For large values of $q$ we establish that the points of a minimal $q$-design are uniformly distributed on the sphere. We construct a weighted cubature formula on the sphere with the minimum number of nodes.

DOI: https://doi.org/10.4213/im661

Full text: PDF file (1416 kB)
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English version:
Izvestiya: Mathematics, 2005, 69:5, 1061–1079

Bibliographic databases:

UDC: 517.5
MSC: 05B30, 65D32, 05B40, 05E35, 33C45
Received: 27.11.2003

Citation: V. A. Yudin, “Distribution of the points of a design on the sphere”, Izv. RAN. Ser. Mat., 69:5 (2005), 205–224; Izv. Math., 69:5 (2005), 1061–1079

Citation in format AMSBIB
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    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. Bannai Eiichi, Bannai Etsuko, “A survey on spherical designs and algebraic combinatorics on spheres”, European J. Combin., 30:6 (2009), 1392–1425  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. R. Alimov, I. G. Tsar'kov, “Chebyshev centres, Jung constants, and their applications”, Russian Math. Surveys, 74:5 (2019), 775–849  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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