{"paper":{"title":"Nikolskii constants for polynomials on the unit sphere","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":"2017-08-31T17:42:31Z","abstract_excerpt":"This paper studies the asymptotic behavior of the exact constants of the Nikolskii inequalities for the space $\\Pi_n^d$ of spherical polynomials of degree at most $n$ on the unit sphere $\\mathbb{S}^d\\subset \\mathbb{R}^{d+1}$ as $n\\to\\infty$. It is shown that for $0<p<\\infty$, \\[ \\lim_{n\\to \\infty} \\sup\\Bigl\\{\\frac{\\|P\\|_{L^\\infty(\\mathbb{S}^d)}}{n^{\\frac dp}\\|P\\|_{L^p(\\mathbb{S}^d)}}:\\ \\ P\\in\\Pi_n^d\\Bigr\\} =\\sup\\Bigl\\{ \\frac{\\|f\\|_{L^\\infty(\\mathbb{R}^{d})}}{\\|f\\|_{L^p(\\mathbb{R}^d)}}:\\ \\ f\\in\\mathcal{E}_p^d \\Bigr\\}, \\] where $\\mathcal{E}_p^d$ denotes the space of all entire functions of spher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09837","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"}