{"paper":{"title":"Global (and Local) Analyticity for Second Order Operators Constructed from Rigid Vector Fields on Products of Tori","license":"","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"David S. Tartakoff","submitted_at":"1994-11-30T22:27:24Z","abstract_excerpt":"We prove global analytic hypoellipticity on a product of tori for partial differential operators which are constructed as rigid (variable coefficient) quadratic polynomials in real vector fields satisfying the H\\\"ormander condition and where $P$ satisfies a `maximal' estimate. We also prove an analyticity result that is local in some variables and global in others for operators whose prototype is\n  $$ P= \\left({\\partial \\over {\\partial x_1}}\\right)^2 + \\left({\\partial \\over {\\partial x_2}}\\right)^2 + \\left(a(x_1,x_2){\\partial \\over {\\partial t}}\\right)^2.$$\n (with analytic $a(x), a(0)=0,$ natu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9411202","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"}