Riesz extremal measures on the sphere for axis-supported external fields

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:356

Article

Brauchart, J. S.¹  Dragnev, P. D.²  Saff, E. B.¹ 

[1] Vanderbilt Univ, Dept Math, Ctr Construct Approximat, Nashville, TN 37240 USA

[2] Indiana Univ Purdue Univ, Dept Math Sci, Ft Wayne, IN 46805 USA

关键词: Balayage;    Equilibrium measures;    Extremal measures;    Minimum energy;    Riesz kernel;    Weighted energy;   

DOI  :  10.1016/j.jmaa.2009.03.060

来源: Elsevier

【 摘 要 】

We investigate the minimal Riesz s-energy problem for positive measures on the d-dimensional unit sphere S-d in the presence of an external field induced by a point charge, and more generally by a line charge. The model interaction is that of Riesz potentials vertical bar x - y vertical bar(-s) with d - 2 <= s < d. For a given axis-supported external field, the support and the density of the corresponding extremal measure on S-d is determined. The special case s = d - 2 yields interesting phenomena, which we investigate in detail. A weak* asymptotic analysis is provided as s -> (d - 2)(+). (c) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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