{"paper":{"title":"Separation of zeros and a Hermite interpolation based frame algorithm for band limited functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Antony Selvan, R. Radha","submitted_at":"2015-11-02T06:34:22Z","abstract_excerpt":"It is shown that if a non-zero function $f\\in B_\\sigma$ has infinitely many double zeros on the real axis, then there exists at least one pair of consecutive zeros whose distance apart is greater than $\\dfrac{\\pi}{\\sigma}\\tau^{1/4}$, $\\tau\\approx5.0625$. A frame algorithm is provided for reconstructing a function $f\\in B_\\sigma$ from its nonuniform samples $\\{f^{(j)}(x_i):j=0,1,\\dots, k-1, i\\in\\mathbb{Z}\\}$ with maximum gap condition, $\\sup\\limits_i(x_{i+1}-x_i)=\\delta<\\dfrac{1}{\\sigma}c_k^{1/2k}$, where $c_k$ is a Wirtinger-Sobolev constant, using Hermite interpolation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04007","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"}