{"paper":{"title":"Riesz sequences and arithmetic progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexander Olevskii, Itay Londner","submitted_at":"2014-04-07T14:25:01Z","abstract_excerpt":"Given a set $\\mathcal{S}$ of positive measure on the circle and a set of integers $\\Lambda$, one may consider the family of exponentials $E\\left(\\Lambda\\right):=\\left\\{ e^{i\\lambda t}\\right\\}_{\\lambda\\in\\Lambda}$ and ask whether it is a Riesz sequence in the space $L^{2}\\left(\\mathcal{S}\\right)$. We focus on this question in connection with some arithmetic properties of the set of frequencies. Improving a result of Bownik and Speegle, we construct a set $\\mathcal{S}$ such that $E\\left(\\Lambda\\right)$ is never a Riesz sequence if $\\Lambda$ contains arbitrary long arithmetic progressions of leng"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1796","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"}