{"paper":{"title":"Global wave-front sets of Banach, Fr{\\'e}chet and Modulation space types, and pseudo-differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Joachim Toft, Karoline Johansson, Sandro Coriasco","submitted_at":"2009-12-17T11:01:17Z","abstract_excerpt":"We introduce global wave-front sets $\\operatorname{WF}_{{\\mathcal B}} (f)$, $f\\in {\\mathscr S}^\\prime(\\textbf{R}^d)$, with respect to suitable Banach or Fr\\'echet spaces ${\\mathcal B}$. An important special case is given by the modulation spaces ${\\mathcal B}=M(\\omega,\\mathscr B)$, where $\\omega$ is an appropriate weight function and $\\mathscr B$ is a translation invariant Banach function space. We show that the standard properties for known notions of wave-front set extend to $\\operatorname{WF}_{{\\mathcal B}} (f)$. In particular, we prove that micro locality and microellipticity hold for a cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.3366","kind":"arxiv","version":3},"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"}