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Riesz Spherical Potentials with External Fields and Minimal Energy Points Separation

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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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Indiana-Purdue University, Fort Wayne, IN, 46805, USA

    P. D. Dragnev

  2. Center for Constructive Approximation, Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA

    E. B. Saff

Authors
  1. P. D. Dragnev
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  2. E. B. Saff
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Correspondence to P. D. Dragnev.

Additional information

The work of P.D. Dragnev was initiated while visiting Vanderbilt University.

Research supported, in part, by a National Science Foundation Research grant DMS 0532154.

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Dragnev, P.D., Saff, E.B. Riesz Spherical Potentials with External Fields and Minimal Energy Points Separation. Potential Anal 26, 139–162 (2007). https://doi.org/10.1007/s11118-006-9032-2

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  • DOI: https://doi.org/10.1007/s11118-006-9032-2

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