概率标架势的极小化
Minimization of the Probabilistic p-frame Potential
摘要：
研究了一类势函数在单位球面上n个点的最优构形。特别是，我们描述这些最佳配置在框架理论的近似性质。此外，我们考虑类似的最佳配置的广义过程的点在球体上的随机分布。在这种概率设置中，我们通过特殊类别的概率框架来表征这些最优分布。我们的工作也表明统计形状分析和框架理论之间的一些联系。
英文摘要：
We investigate the optimal configurations of n points on the unit sphere for a class of potential functions. In particular, we characterize these optimal configurations in terms of their approximation properties within frame theory. Furthermore, we consider similar optimal configurations in terms of random distributions of points on the sphere. In this probabilistic setting, we characterize these optimal distributions by means of special classes of probabilistic frames. Our work also indicates some connections between statistical shape analysis and frame theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
