Bounds on energy and potentials of discrete measures on the sphere

Autor:	Borodachov, S., Boyvalenkov, P., Dragnev, P., Hardin, D., Saff, E., Stoyanova, M.
Rok vydání:	2024
Předmět:	Mathematics - Metric Geometry Mathematics - Classical Analysis and ODEs Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	We establish upper and lower universal bounds for potentials of weighted designs on the sphere $\mathbb{S}^{n-1}$ that depend only on quadrature nodes and weights derived from the design structure. Our bounds hold for a large class of potentials that includes absolutely monotone functions. The classes of spherical designs attaining these bounds are characterized. Additionally, we study the problem of constrained energy minimization for Borel probability measures on $\mathbb{S}^{n-1}$ and apply it to optimal distribution of charge supported at a given number of points on the sphere. In particular, our results apply to $p$-frame energy. Comment: 21 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.07442 Zobrazit plný text záznamu View this record from Arxiv