{"paper":{"title":"Almost periodic pseudodifferential operators and Gevrey classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Alessandro Oliaro, Luigi Rodino, Patrik Wahlberg","submitted_at":"2011-02-22T17:06:39Z","abstract_excerpt":"We study almost periodic pseudodifferential operators acting on almost periodic functions $G_{\\rm ap}^s(\\rr d)$ of Gevrey regularity index $s \\geq 1$. We prove that almost periodic operators with symbols of H\\\"ormander type $S_{\\rho,\\delta}^m$ satisfying an $s$-Gevrey condition are continuous on $G_{\\rm ap}^s(\\rr d)$ provided $0 < \\rho \\leq 1$, $\\delta=0$ and $s \\rho \\geq 1$. A calculus is developed for symbols and operators using a notion of regularizing operator adapted to almost periodic Gevrey functions and its duality. We apply the results to show a regularity result in this context for a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4553","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"}