LeVeque type inequalities and discrepancy estimates for minimal energy configurations on spheres
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 .
LeVeque type inequalities, discrepancy, minimal energy, spherical harmonics
Narcowich, Francis J., Xingping Sun, Joseph D. Ward, and Z. Wu. "LeVeque type inequalities and discrepancy estimates for minimal energy configurations on spheres." Journal of Approximation Theory 162, no. 6 (2010): 1256-1278.