Note on a Generalized Invariance Principle and its Relevance for Cap Discrepancy and Energy
We give an extension of Stolarsky’s invariance principle. For a certain class of energy kernel functions we show relations between the spherical cap discrepancy and the energy of N—point sets on the unit sphere. We see that cap discrepancy and energy are comparable in a sense. In addition an integral representation for the energy which involves discrepancy functions is derived.
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