{"paper":{"title":"A bridge between U-frequent hypercyclicity and frequent hypercyclicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.DS","authors_text":"Quentin Menet","submitted_at":"2019-04-09T17:57:22Z","abstract_excerpt":"Given $\\mathcal{A}$ the family of weights $a=(a_n)_n$ decreasing to $0$ such that the series $\\sum_{n=0}^{\\infty} a_n$ diverges, we show that the supremum on $\\mathcal{A}$ of lower weighted densities coincides with the unweighted upper density and that the infimum on $\\mathcal{A}$ of upper weighted densities coincides with the unweighted lower density. We then investigate the notions of $\\mathcal{U}$-frequent hypercyclicity and frequent hypercyclicity associated to these weighted densities. We show that there exists an operator which is $\\mathcal{U}$-frequently hypercyclic for each weight in $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04818","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"}