{"paper":{"title":"Convergence properties of spline-like cardinal interpolation operators acting on $l^p$ data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jeff Ledford","submitted_at":"2013-12-14T16:42:06Z","abstract_excerpt":"If $f\\in \\{f\\in L^p(\\mathbb{R}): f(x)=\\int_{-\\pi}^{\\pi}e^{ix\\xi}d\\beta(\\xi), \\beta\\in B.V.([-\\pi,\\pi]) \\}$, then $f$ is determined by its samples on the integers by taking an appropriate limit. Specifically, $\\| f - L_{\\phi_\\alpha}f \\|_{L^p(\\mathbb{R})}\\to 0$ as $\\alpha\\to\\infty$ provided that $\\{\\phi_\\alpha: \\alpha\\in A\\}$ is what we call a spline-like family of cardinal interpolators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4062","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"}