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 \(d\).
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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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Communicated by Edward B. Saff.
This work was carried out during the tenure of an ERCIM “Alain Bensoussan” Fellowship Program. The research leading to these results received funding from the European Union Seventh Framework Program (FP7/2007-2013) under grant agreement no. 246016.
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Bondarenko, A., Radchenko, D. & Viazovska, M. Well-Separated Spherical Designs. Constr Approx 41, 93–112 (2015). https://doi.org/10.1007/s00365-014-9238-2
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DOI: https://doi.org/10.1007/s00365-014-9238-2
Keywords
- Spherical designs
- Well-separated configurations
- Topological degree
- Marcinkiewicz–Zygmund inequality
- Area-regular partitions