{"paper":{"title":"Global Gevrey hypoellipticity on the torus for a class of systems of complex vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexandre Arias Junior, Alexandre Kirilov, Cleber de Medeira","submitted_at":"2018-10-03T18:35:52Z","abstract_excerpt":"Let $L_j = \\partial_{t_j} + (a_j+ib_j)(t_j) \\partial_x, \\, j = 1, \\dots, n,$ be a system of vector fields defined on the torus $\\mathbb{T}_t^{n}\\times\\mathbb{T}_x^1$, where the coefficients $a_j$ and $b_j$ are real-valued functions belonging to the Gevrey class $G^s(\\mathbb{T}^1)$, with $s>1$. In this paper we were able to characterize the global $s-$hypoellipticity of this system in terms of Diophantine approximations and the Nirenberg-Treves condition (P)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01906","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"}