Riesz Spherical Potentials with External Fields and Minimal Energy Points Separation

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• 作者：P. D. Dragnev and E. B. Saff
• 关键词：minimal energy problems with external fields ; Riesz spherical potentials ; minimal s ; energy points separation ; balayage ; α ; superharmonic functions
• 刊名：Potential Analysis
• 出版年：2007
• 出版时间：March, 2007
• 年：2007
• 卷：26
• 期：2
• 页码：139-162
• 全文大小：504 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Potential Theory
  Probability Theory and Stochastic Processes
  Geometry
  Functional Analysis
  
• 出版者：Springer Netherlands
• ISSN：1572-929X

文摘

In this paper we consider the minimal energy problem on the sphere S d for Riesz potentials with external fields. Fundamental existence, uniqueness, and characterization results are derived about the associated equilibrium measure. The discrete problem and the corresponding weighted Fekete points are investigated. As an application we obtain the separation of the minimal s-energy points for d – 2 < s < d. The explicit form of the separation constant is new even for the classical case of s = d – 1.