Riesz polarization inequalities in higher dimensions

作者：Erdelyi Tamas; Saff Edward B^*

来源：Journal of Approximation Theory, 2013, 171: 128-147.

DOI：10.1016/j.jat.2013.03.003

• Chebyshev constants
• Polarization inequalities
• Riesz energy
• Potentials

We derive bounds and asymptotics for the maximum Riesz polarization quantity
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(which is n times the Chebyshev constant) for quite general sets A subset of R-m with special focus on the Unit sphere and unit ball. We combine elementary averaging arguments with potential theoretic tools to formulate and prove our results. We also give a discrete version of the recent result of Hardin, Kendall, and Saff which solves the Riesz polarization problem for the case when A is the unit circle and p > 0, as well as provide an independent proof of their result for p = 4 that exploits classical polynomial inequalities and yields new estimates. Furthermore, we raise some challenging conjectures.

• 出版日期2013-7