{"paper":{"title":"Covering and separation of Chebyshev points for non-integrable Riesz potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexander Reznikov, Alexander Volberg, Edward B. Saff","submitted_at":"2017-03-01T02:26:28Z","abstract_excerpt":"For Riesz $s$-potentials $K(x,y)=|x-y|^{-s}$, $s>0$, we investigate separation and covering properties of $N$-point configurations $\\omega^*_N=\\{x_1, \\ldots, x_N\\}$ on a $d$-dimensional compact set $A\\subset \\mathbb{R}^\\ell$ for which the minimum of $\\sum_{j=1}^N K(x, x_j)$ is maximal. Such configurations are called $N$-point optimal Riesz $s$-polarization (or Chebyshev) configurations. For a large class of $d$-dimensional sets $A$ we show that for $s>d$ the configurations $\\omega^*_N$ have the optimal order of covering. Furthermore, for these sets we investigate the asymptotics as $N\\to \\inft"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00106","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}