{"paper":{"title":"On the endomorphisms of some sheaves of functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Patrice P. Ntumba","submitted_at":"2013-02-22T07:55:34Z","abstract_excerpt":"Given a $C^\\infty$ real manifold $X$ and $\\mathcal{C}^m_X$ its sheaf of $m$-times differentiable real-valued functions, we prove that the sheaf $\\mathcal{D}^{m, r}_X$ of differential operators of order $\\leq m$ with coefficient functions of class $C^r$ can be obtained in terms of the sheaf $\\mathcal{H}om_{\\mathbb{R}_X}(\\mathcal{C}^m_X, \\mathcal{C}^r_X)$ of morphisms of $\\mathcal{C}^m_X$ into $\\mathcal{C}^r_X$. The superscripts $m$ and $r$ are integers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5506","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"}