{"paper":{"title":"Orthogonal polynomials associated with equilibrium measures on $\\mathbb{R}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"G\\\"okalp Alpan","submitted_at":"2016-03-24T18:54:39Z","abstract_excerpt":"Let $K$ be a non-polar compact subset of $\\mathbb{R}$ and $\\mu_K$ denote the equilibrium measure of $K$. Furthermore, let $P_n\\left(\\cdot, \\mu_K\\right)$ be the $n$-th monic orthogonal polynomial for $\\mu_K$. It is shown that $\\|P_n\\left(\\cdot, \\mu_K\\right)\\|_{L^2(\\mu_K)}$, the Hilbert norm of $P_n\\left(\\cdot, \\mu_K\\right)$ in $L^2(\\mu_K)$, is bounded below by $\\mathrm{Cap}(K)^n$ for each $n\\in\\mathbb{N}$. A sufficient condition is given for $\\displaystyle\\left(\\|P_n\\left(\\cdot;\\mu_K\\right)\\|_{L^2(\\mu_K)}/\\mathrm{Cap}(K)^n\\right)_{n=1}^\\infty$ to be unbounded. More detailed results are presente"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07705","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"}