{"paper":{"title":"Periodicity of the spectrum in dimension one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Alex Iosevich, Mihail N. Kolountzakis","submitted_at":"2011-08-29T18:22:09Z","abstract_excerpt":"A bounded measurable set $\\Omega$, of Lebesgue measure 1, in the real line is called spectral if there is a set $\\Lambda$ of real numbers (\"frequencies\") such that the exponential functions $e_\\lambda(x) = \\exp(2\\pi i \\lambda x)$, $\\lambda\\in\\Lambda$, form a complete orthonormal system of $L^2(\\Omega)$. Such a set $\\Lambda$ is called a {\\em spectrum} of $\\Omega$. In this note we prove that any spectrum $\\Lambda$ of a bounded measurable set $\\Omega\\subseteq\\RR$ must be periodic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5689","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"}