{"paper":{"title":"On polynomial functions on non-conmmutative groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"E. V. Shulman, J. M. Almira","submitted_at":"2016-12-12T18:07:43Z","abstract_excerpt":"Let $G$ be a topological group. We investigate relations between two classes of \"polynomial like\" continuous functions on $G$ defined, respectively, by the conditions (1) $\\Delta_h^{n+1}f=0$ for every $h \\in G$, and (2) $\\Delta_{h_{n+1}} \\Delta_{h_{n}}\\cdots \\Delta_{h_{1}}f=0$, for every $h_1,\\cdots, h_{n+1} \\in G$. It is shown that for many (but not all) groups these classes coincide. We consider also Montel type versions of the above conditions - when (1) and (2) hold only for steps $h$ in a generating subset of $G$. Our approach is based on the study of the counterparts of the discussed cla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03826","kind":"arxiv","version":3},"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"}