Abstract
In this paper we elaborate on the interplay between energy optimization, positive definiteness, and discrepancy. In particular, assuming the existence of a K-invariant measure μ with full support, we show that conditional positive definiteness of a kernel K is equivalent to a long list of other properties: including, among others, convexity of the energy functional, inequalities for mixed energies, and the fact that μ minimizes the energy integral in various senses. In addition, we prove a very general form of the Stolarsky Invariance Principle on compact spaces, which connects energy minimization and discrepancy and extends several previously known versions.
Originalsprache | englisch |
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Aufsatznummer | 126220 |
Fachzeitschrift | Journal of Mathematical Analysis and Applications |
Jahrgang | 513 |
Ausgabenummer | 2 |
DOIs | |
Publikationsstatus | Veröffentlicht - 2022 |