Asymptotics of Discrete Riesz d-Polarization on Subsets of d-Dimensional Manifolds

S. V. Borodachov; N. Bosuwan

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Asymptotics of Discrete Riesz d-Polarization on Subsets of d-Dimensional Manifolds

机译：d维流形子集上的离散Riesz d极化的渐近性

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We prove a conjecture of T. Erdélyi and E.B. Saff, concerning the form of the dominant term (as N→∞) of the N-point Riesz d-polarization constant for an infinite compact subset A of a d-dimensional C~1-manifold embedded in R~m (d ≤ m). Moreover, if we assume further that the d-dimensional Hausdorff measure of A is positive, we show that any asymptotically optimal sequence of Npoint configurations for the N-point d-polarization problem on A is asymptotically uniformly distributed with respect to H_(d|A). These results also hold for finite unions of such sets A provided that their pairwise intersections have H_d-measure zero.

机译：我们证明了T.Erdélyi和E.B. Saff，涉及嵌入到R〜m中的d维C〜1流形的无穷紧子集A的N点Riesz d极化常数的主导项（从N→∞的形式）（d≤m ）。此外，如果我们进一步假设A的d维Hausdorff测度为正，则表明对于A上的N点d极化问题，任何N点配置的渐近最优序列相对于H_（d |渐近均匀分布）。一种）。这些结果也适用于此类集合A的有限并集，条件是它们的成对交点的H_d度量为零。

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《Potential analysis: An international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis》 |2014年第1期|共15页
作者
S. V. Borodachov; N. Bosuwan;
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正文语种 eng
中图分类数学;
关键词
Riesz polarization; Chebyshev constants; Riesz energy; Potentials;

机译：Riesz极化;Chebyshev常数;Riesz能量;势;

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1. Asymptotics of Discrete Riesz d-Polarization on Subsets of d-Dimensional Manifolds [J] . S. V. Borodachov, N. Bosuwan Potential analysis: An international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis . 2014,第1期

机译：d维流形子集上的离散Riesz d极化的渐近性
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7. Asymptotics of discrete Riesz $d$-polarization on subsets of $d$-dimensional manifolds [O] . Borodachov, S. V., Bosuwan, N. 2013

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Asymptotics of Discrete Riesz d-Polarization on Subsets of d-Dimensional Manifolds

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