Riesz polarization inequalities in higher dimensions Academic Article uri icon

abstract

  • We derive bounds and asymptotics for the maximum Riesz polarization quantity (which is n times the Chebyshev constant) for quite general sets A⊂Rm 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. © 2013 Elsevier Inc.

author list (cited authors)

  • Erdélyi, T., & Saff, E. B.

citation count

  • 12

publication date

  • July 2013