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Constructive Approximation

, Volume 41, Issue 1, pp 93–112 | Cite as

Well-Separated Spherical Designs

  • Andriy Bondarenko
  • Danylo Radchenko
  • Maryna Viazovska
Article

Abstract

For each \(N\ge C_dt^d\), we prove the existence of a well-separated spherical \(t\)-design in the sphere \(S^d\) consisting of \(N\) points, where \(C_d\) is a constant depending only on \(d\).

Keywords

Spherical designs Well-separated configurations Topological degree Marcinkiewicz–Zygmund inequality Area-regular partitions 

Mathematics Subject Classification

52C35 41A55 41A05 41A63 

Notes

Acknowledgments

The authors thank the Mathematisches Forschungsinstitut Oberwolfach for their hospitality during the preparation of this manuscript and for providing a stimulating atmosphere for research. This paper is partially supported by the Centre for Advanced Study at the Norwegian Academy of Science and Letters in Oslo and grant MTM2011-27637.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Andriy Bondarenko
    • 1
    • 2
  • Danylo Radchenko
    • 1
    • 3
  • Maryna Viazovska
    • 3
  1. 1.Department of Mathematical AnalysisTaras Shevchenko National University of KyivKyivUkraine
  2. 2.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway
  3. 3.Max Planck Institute for MathematicsBonnGermany

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