{"paper":{"title":"Compactness Criteria for Sets and Operators in the Setting of Continuous Frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"D. Parra, M. Mantoiu","submitted_at":"2013-01-02T15:34:16Z","abstract_excerpt":"To a generalized tight continuous frame in a Hilbert space $\\H$ indexed by a locally compact space $\\Si$ endowed with a Radon measure, one associates a coorbit theory converting spaces of functions on $\\Si$ in spaces of vectors comparable with $\\H$. If the continuous frame is provided by the action of a suitable family of bounded operators on a fixed window, a symbolic calculus emerges, assigning operators in $\\H$ to functions on $\\Si$. We give some criteria of relative compactness for sets and for families of compact operators, involving tightness properties in terms of objects canonically as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0247","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"}