Equidistribution on the Sphere
SIAM Journal on Scientific Computing
Equidistribution and extremal energy of N points on the sphere
Modelling and computation for applications in mathematics, science, and engineering
Estimates for the discrepancy of a signed measure using its energy norm
Journal of Approximation Theory
Energy functionals, numerical integration and asymptotic equidistribution on the sphere
Journal of Complexity
On separation of minimal Riesz energy points on spheres in Euclidean spaces
Journal of Computational and Applied Mathematics - Special issue: Special functions in harmonic analysis and applications
Discrepancy, separation and Riesz energy of finite point sets on the unit sphere
Advances in Computational Mathematics
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Representations for the Riesz kernel | x-y | - s are presented, which lead to new interpretations of the energy of measures. It is shown that the surface measure on the unit sphere in R d solves a minimal energy problem independent of s (but intimately related to Riesz s -energy) and that n points on the unit circle with minimal discrete Riesz energy are n th roots of unity, unique up to rotation. Moreover, the energy of signed measures is estimated in terms of their discrepancy.