{"paper":{"title":"A minimum principle for potentials with application to Chebyshev constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Reznikov, E. B. Saff, O. V. Vlasiuk","submitted_at":"2016-07-25T14:14:49Z","abstract_excerpt":"For \"Riesz-like\" kernels $K(x,y)=f(|x-y|)$ on $A\\times A$, where $A$ is a compact $d$-regular set $A\\subset \\mathbb{R}^p$, we prove a minimum principle for potentials $U_K^\\mu=\\int K(x,y)d\\mu(x)$, where $\\mu$ is a Borel measure supported on $A$. Setting $P_K(\\mu)=\\inf_{y\\in A}U^\\mu(y)$, the $K$-polarization of $\\mu$, the principle is used to show that if $\\{\\nu_N\\}$ is a sequence of measures on $A$ that converges in the weak-star sense to the measure $\\nu$, then $P_K(\\nu_N)\\to P_K(\\nu)$ as $N\\to \\infty$. The continuous Chebyshev (polarization) problem concerns maximizing $P_K(\\mu)$ over all pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07283","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"}