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

Abstract

Let denote the unit sphere in the Euclidean space . We develop LeVeque type inequalities for the discrepancy between the rotationally invariant probability measure and the normalized counting measures on . 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 .

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1016/j.jat.2010.01.003

Keywords

LeVeque type inequalities, discrepancy, minimal energy, spherical harmonics

Publication Date

2010

Journal Title

Journal of Approximation Theory

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