{"paper":{"title":"Estimates of the asymptotic Nikolskii constants for spherical polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dmitry Gorbachev, Feng Dai, Sergey Tikhonov","submitted_at":"2019-07-08T19:55:17Z","abstract_excerpt":"Let $\\Pi_n^d$ denote the space of spherical polynomials of degree at most $n$ on the unit sphere $\\mathbb{S}^d\\subset \\mathbb{R}^{d+1}$ that is equipped with the surface Lebesgue measure $d\\sigma$ normalized by $\\int_{\\mathbb{S}^d} \\, d\\sigma(x)=1$. This paper establishes a close connection between the asymptotic Nikolskii constant, $$ \\mathcal{L}^\\ast(d):=\\lim_{n\\to \\infty} \\frac 1 {\\dim \\Pi_n^d} \\sup_{f\\in \\Pi_n^d} \\frac { \\|f\\|_{L^\\infty(\\mathbb{S}^d)}}{\\|f\\|_{L^1(\\mathbb{S}^d)}},$$ and the following extremal problem: $$ \\mathcal{I}_\\alpha:=\\inf_{a_k} \\Bigl\\| j_{\\alpha+1} (t)- \\sum_{k=1}^\\i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03832","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"}