{"paper":{"title":"Liftings for ultra-modulation spaces, and one-parameter groups of Gevrey type pseudo-differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ahmed Abdeljawad, Joachim Toft, Sandro Coriasco","submitted_at":"2017-12-09T15:32:15Z","abstract_excerpt":"We deduce one-parameter group properties for pseudo-differential operators $\\operatorname{Op} (a)$, where $a$ belongs to the class $\\Gamma ^{(\\omega _0)}_*$ of certain Gevrey symbols. We use this to show that there are pseudo-differential operators $\\operatorname{Op} (a)$ and $\\operatorname{Op} (b)$ which are inverses to each others, where $a\\in \\Gamma ^{(\\omega _0)}_*$ and $b\\in \\Gamma ^{(1/\\omega _0)}_*$.\n  We apply these results to deduce lifting property for modulation spaces and construct explicit isomorpisms between them. For each weight functions $\\omega ,\\omega _0$ moderated by GRS sub"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04338","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"}