{"paper":{"title":"A new sampling density condition for shift-invariant spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Antony Selvan","submitted_at":"2017-02-01T09:19:16Z","abstract_excerpt":"Let $X=\\{x_i:i\\in\\mathbb{Z}\\}$, $\\dots<x_{i-1}<x_i<x_{i+1}<\\dots$, be a sampling set which is separated by a constant $\\gamma>0$. Under certain conditions on $\\phi$, it is proved that if there exists a positive integer $\\nu$ such that $$\\delta_\\nu:=\\sup\\limits_{i\\in\\mathbb{Z}}(x_{i+\\nu}-x_i)<\\dfrac{\\nu}{2\\pi}\\left(\\dfrac{c_{k}^2}{M_{2k}}\\right)^{\\frac{1}{4k}},$$ then every function belonging to a shift-invariant space $V(\\phi)$ can be reconstructed stably from its nonuniform sample values $\\{f^{(j)}(x_i):j=0,1,\\dots, k-1, i\\in\\mathbb{Z}\\}$, where $c_k$ is a Wirtinger-Sobolev constant and $M_{2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00170","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"}