Bounds on Discrete Potentials of Spherical (k,k)-Designs

Autor:	Borodachov, S., Boyvalenkov, P., Saff, P. Dragnev. D. Hardin. E., Stoyanova, M.
Rok vydání:	2024
Předmět:	Mathematics - Metric Geometry Mathematics - Classical Analysis and ODEs Mathematics - Combinatorics 52C35 05B30
Druh dokumentu:	Working Paper
Popis:	We derive universal lower and upper bounds for max-min and min-max problems (also known as polarization) for the potential of spherical $(k,k)$-designs and provide certain examples, including unit-norm tight frames, that attain these bounds. The universality is understood in the sense that the bounds hold for all spherical $(k,k)$-designs and for a large class of potential functions, and the bounds involve certain nodes and weights that are independent of the potential. When the potential function is $h(t)=t^{2k}$, we prove an optimality property of the spherical $(k,k)$-designs in the class of all spherical codes of the same cardinality both for max-min and min-max potential problems. Comment: 21 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.00290 Zobrazit plný text záznamu View this record from Arxiv