{"paper":{"title":"Kadec-1/4 Theorem for Sinc Bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Antonio Avantaggiati, Paola Loreti, Pierluigi Vellucci","submitted_at":"2016-03-29T13:20:45Z","abstract_excerpt":"In this paper we show two results. In the first result we consider $\\lambda_n-n=\\frac{A}{n^\\alpha}$ for $n\\in\\mathbb N$; if $\\alpha>1/2$ and $0<A<\\frac{1}{\\pi\\sqrt{2 \\sqrt{2}\\zeta(2\\alpha)}}$, the system $\\left\\{\\operatorname{sinc}( \\lambda_n - t)\\right\\}_{n\\in\\mathbb N}$ is a Riesz basis for $PW_{\\pi}$. With the second result, we study the stability of $\\left\\{\\operatorname{sinc}( \\lambda_n - t)\\right\\}_{n\\in\\mathbb Z}$ for $\\lambda_n\\in\\mathbb C$; if $|\\lambda_n-n|\\leqq L<\\frac{1}{\\pi}\\, \\sqrt\\frac{3\\alpha}{8}$, for all $n\\in\\mathbb Z$, then $\\{\\operatorname{sinc}(\\lambda_n-t)\\}_{n\\in\\mathbb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08762","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"}