The minimizers of the p-frame potential

doi:10.1016/j.acha.2020.04.003

	The minimizers of the p-frame potential
	Xu, Zhiqiang 1,2; Xu, Zili 1,2
刊名	APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
	2021-05-01
卷号	52 页码:366-379
关键词	Frame potential Tight frames Spherical designs
ISSN号	1063-5203
DOI	10.1016/j.acha.2020.04.003
英文摘要	For any positive real number p, the p-frame potential of N unit vectors X := {x(1), ..., x(N)} subset of R-d is defined as FP (p,N,d) (X) = Sigma(i not equal j) vertical bar < x(i), x(j))vertical bar >(p). In this paper, we focus on this quantity for N = d + 1 points and establish uniqueness of minimizers of FP (p,d+1, d) for all p is an element of (0, 2). Our results completely solve the minimization problem of the p-frame potential when N = d + 1, confirming a conjecture posed by Chen, Gonzales, Goodman, Kang and Okoudjou [4]. (C) 2020 Elsevier Inc. All rights reserved.
资助项目	Beijing Natural Science Foundation[Z180002] ; NSFC[11688101] ; NSFC[91630203]
WOS研究方向	Mathematics
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000620925100013
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/58209]
专题	中国科学院数学与系统科学研究院
通讯作者	Xu, Zili
作者单位	1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Comp Math, LSEC, Beijing 100091, Peoples R China
推荐引用方式 GB/T 7714	Xu, Zhiqiang,Xu, Zili. The minimizers of the p-frame potential[J]. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS,2021,52:366-379.
APA	Xu, Zhiqiang,&Xu, Zili.(2021).The minimizers of the p-frame potential.APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS,52,366-379.
MLA	Xu, Zhiqiang,et al."The minimizers of the p-frame potential".APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 52(2021):366-379.