{"paper":{"title":"Characterization of derivations through their actions on certain elementary functions","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Eszter Gselmann","submitted_at":"2013-07-16T13:54:54Z","abstract_excerpt":"The main aim of this note is to provide characterization theorems concerning real derivations. Among others the following implication will be verified: Assume that $\\xi\\colon \\mathbb{R}\\to \\mathbb{R}$ is a given differentiable function and for the additive function $d\\colon \\mathbb{R}\\to \\mathbb{R}$, the mapping \\[ x\\longmapsto d(\\xi(x))-\\xi'(x)d(x) \\] is regular (e. g. measurable, continuous, locally bounded). Then $d$ is a sum of a derivation and a linear function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4277","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"}