{"paper":{"title":"Derivations and linear functions along rational functions","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Eszter Gselmann","submitted_at":"2013-07-02T09:13:09Z","abstract_excerpt":"The main purpose of this paper is to give characterization theorems on derivations as well as on linear functions. Among others the following problem will be investigated: Let $n\\in\\mathbb{Z}$, $f, g\\colon\\mathbb{R}\\to\\mathbb{R}$ be additive functions, $<{array}{cc} a&b c&d {array}>\\in\\mathbf{GL}_{2}(\\mathbb{Q})$ be arbitrarily fixed, and let us assume that the mapping \\[\n  \\phi(x)=g<\\frac{ax^{n}+b}{cx^{n}+d}>-\\frac{x^{n-1}f(x)}{(cx^{n}+d)^{2}} \\quad <x\\in\\mathbb{R}, cx^{n}+d\\neq 0> \\] satisfies some regularity on its domain (e.g. (locally) boundedness, continuity, measurability). Is it true t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0634","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"}