{"paper":{"title":"A zero-sqrt(5)/ 2 law for cosine families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jean Esterle (IMB)","submitted_at":"2015-05-22T13:24:44Z","abstract_excerpt":"Let $a \\in \\R,$ and let $k(a)$ be the largest constant such that $sup\\vert cos(na)-cos(nb)\\vert \\textless{} k(a)$ for $b\\in \\R$ implies that $b \\in \\pm a+2\\pi\\Z. $ We show that\nif a cosine sequence $(C(n))\\_{n\\in \\Z}$ with values in a Banach algebra $A$ satisfies $sup\\_{n\\ge 1}\\Vert C(n) -cos(na).1\\_A\\Vert \\textless{} k(a),$ then $C(n)=cos(na)$ for $n\\in \\Z.$ Since\n${\\sqrt 5\\over 2} \\le k(a) \\le {8\\over 3\\sqrt 3}$ for every $a \\in \\R,$ this shows that if some cosine family $(C(g))\\_{g\\in G}$ over an abelian group $G$ in a Banach algebra satisfies $sup\\_{g\\in G}\\Vert C(g)-c(g)\\Vert \\textless{} "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06064","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"}