Optimal discrete measures for Riesz potentials
Optimal discrete measures for Riesz potentials
复制标题
Riesz 势的最佳离散测量
DOI：
--
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
E. Saff
中科院分区：
文献类型：
--
作者：
S. Borodachov;D. Hardin;Alexander Reznikov;Alexander Reznikov;E. Saff
对于sgeqslant d，我们得到首项为N p的某类d-可求长紧子集的最大权N-点Riesz $s$-极化（或Chebyshev常数）的不确定性.这个类包括$d$-维$C^1$流形的紧致子集，其相对于流形的边界具有$mathcal{H}_d$-测度零，以及当它们的两两相交具有$mathcal{H}_d$-测度零时这些集合的有限并。我们还明确地找到了渐近最优$N$点偏振配置的弱$^*$极限分布为$N 不需要钱。
For $sgeqslant d$, we obtain the leading term as $N o infty$ of the maximal weighted $N$-point Riesz $s$-polarization (or Chebyshev constant) for a certain class of $d$-rectifiable compact subsets of $mathbb{R}^p$. This class includes compact subsets of $d$-dimensional $C^1$ manifolds whose boundary relative to the manifold has $mathcal{H}_d$-measure zero, as well as finite unions of such sets when their pairwise intersections have $mathcal{H}_d$-measure zero. We also explicitly find the weak$^*$ limit distribution of asymptotically optimal $N$-point polarization configurations as $N o infty$.