1. The minimizers of the p-frame potential.
- Author
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Xu, Zhiqiang and Xu, Zili
- Subjects
- *
REAL numbers , *LOGICAL prediction , *PROBLEM solving - Abstract
For any positive real number p , the p -frame potential of N unit vectors X : = { x 1 , ... , x N } ⊂ R d is defined as FP p , N , d (X) = ∑ i ≠ j | 〈 x i , x j 〉 | 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 ∈ (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]. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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