{"paper":{"title":"Hypoellipticity and vanishing theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Gerardo A. Mendoza","submitted_at":"2013-01-24T15:33:50Z","abstract_excerpt":"Let $-\\im\\Lie_\\T$ (essentially Lie derivative with respect to $\\T$, a smooth nowhere zero real vector field) and $P$ be commuting differential operators, respectively of orders 1 and $m\\geq 1$, the latter formally normal, both acting on sections of a vector bundle over a closed manifold. It is shown that if $P+(-i\\Lie_\\T)^m$ is elliptic then the restriction of $-\\im\\Lie_\\T$ to $\\Dom\\subset \\ker P\\subset L^2$ yields a selfadjoint operator $-\\im\\Lie_\\T|_\\Dom:\\Dom\\subset\\ker P\\to \\ker P$ with compact resolvent ($\\Dom$ is specified carefully). It is also shown that, in the presence of an additiona"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5818","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"}