{"paper":{"title":"The Gabor wave front set in spaces of ultradifferentiable functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alessandro Oliaro, Chiara Boiti, David Jornet","submitted_at":"2017-06-26T14:42:10Z","abstract_excerpt":"Given a non-quasianalytic subadditive weight function $\\omega$ we consider the weighted Schwartz space $\\mathcal{S}_\\omega$ and the short-time Fourier transform on $\\mathcal{S}_\\omega$, $\\mathcal{S}'_\\omega$ and on the related modulation spaces with exponential weights. In this setting we define the $\\omega$-wave front set $WF'_\\omega(u)$ and the Gabor $\\omega$-wave front set $WF^G_\\omega(u)$ of $u\\in\\mathcal{S}'_{\\omega}$, and we prove that they coincide. Finally we look at applications of this wave front set for operators of differential and pseudo-differential type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08413","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"}