Abstract
This chapter is devoted to large N asymptotic results for energy and point configurations on the multidimensional sphere \(S^d\) . We begin with a discussion of the property of uniform distribution on the sphere of a sequence of N-point configurations and provide necessary and sufficient conditions for such uniformity in terms of the notion of discrepancy.
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Notes
- 1.
As before, \(\mathcal M_\mathrm{sign}(A)\) denotes the set of finite signed Borel measures supported on a compact set A.
- 2.
Equation (6.8.17) is a special case of the Kampé de Fériet function.
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Borodachov, S.V., Hardin, D.P., Saff, E.B. (2019). Asymptotics for Energy Minimizing Configurations on \(S^d\). In: Discrete Energy on Rectifiable Sets. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-84808-2_6
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DOI: https://doi.org/10.1007/978-0-387-84808-2_6
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