LeVeque type inequalities and discrepancy estimates for minimal energy configurations on spheres

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Abstract

Let Sd denote the unit sphere in the Euclidean space Rd+1(d1). We develop LeVeque type inequalities for the discrepancy between the rotationally invariant probability measure and the normalized counting measures on Sd. We obtain both upper bound and lower bound estimates. We then use these inequalities to estimate the discrepancy of the normalized counting measures associated with minimal energy configurations on Sd.

Keywords

LeVeque type inequalities
Discrepancy
Minimal energy
Spherical harmonics

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