{"paper":{"title":"Global hypoellipticity for a class of pseudo-differential operators on the torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexandre Kirilov, Cleber de Medeira, Fernando de \\'Avila Silva, Rafael Borro Gonzalez","submitted_at":"2016-12-06T21:26:35Z","abstract_excerpt":"We show that an obstruction of number-theoretical nature appears as a necessary condition for the global hypoellipticity of the pseudo-differential operator $L=D_t+(a+ib)(t)P(D_x)$ on $\\mathbb{T}^1_t\\times\\mathbb{T}_x^{N}$. This condition is also sufficient when the symbol $p(\\xi)$ of $P(D_x)$ has at most logarithmic growth. If $p(\\xi)$ has super-logarithmic growth, we show that the global hypoellipticity of $L$ depends on the change of sign of certain interactions of the coefficients with the symbol $p(\\xi).$ Moreover, the interplay between the order of vanishing of coefficients with the orde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02033","kind":"arxiv","version":2},"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"}