{"paper":{"title":"Global regularity for ordinary differential operators with polynomial coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.CA","authors_text":"Fabio Nicola, Luigi Rodino","submitted_at":"2011-06-30T12:24:24Z","abstract_excerpt":"For a class of ordinary differential operators $P$ with polynomial coefficients, we give a necessary and sufficient condition for $P$ to be globally regular in $\\R$, i.e. $u\\in\\cS^\\prime(\\R)$ and $Pu\\in\\cS(\\R)$ imply $u\\in \\cS(\\R)$ (this can be regarded as a global version of the Schwartz' hypoellipticity notion). The condition involves the asymptotic behaviour, at infinity, of the roots $\\xi=\\xi_j(x)$ of the equation $p(x,\\xi)=0$, where $p(x,\\xi)$ is the (Weyl) symbol of $P$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.6203","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"}