{"paper":{"title":"Frames Induced by the Action of Continuous Powers of an Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Akram Aldroubi, Armenak Petrosyan, Longxiu Huang","submitted_at":"2018-01-30T17:19:21Z","abstract_excerpt":"We investigate systems of the form $\\{A^tg:g\\in\\mathcal{G},t\\in[0,L]\\}$ where $A \\in B(\\mathcal{H})$ is a normal operator in a separable Hilbert space $\\mathcal{H}$, $\\mathcal{G}\\subset \\mathcal{H}$ is a countable set, and $L$ is a positive real number. Although the main goal of this work is to study the frame properties of $\\{A^tg:g\\in\\mathcal{G},t\\in[0,L]\\}$, as intermediate steps, we explore the completeness and Bessel properties of such systems from a theoretical perspective, which are of interest by themselves. Beside the theoretical appeal of investigating such systems, their connections"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10103","kind":"arxiv","version":2},"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"}