Riesz Spherical Potentials with External Fields and Minimal Energy Points Separation |
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Authors: | P D Dragnev E B Saff |
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Institution: | (1) Department of Mathematical Sciences, Indiana-Purdue University, Fort Wayne, IN 46805, USA;(2) Center for Constructive Approximation, Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA |
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Abstract: | 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.
Research supported, in part, by a National Science Foundation Research grant DMS 0532154. |
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Keywords: | minimal energy problems with external fields Riesz spherical potentials minimal s-energy points separation balayage α -superharmonic functions |
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