{"paper":{"title":"On a sampling expansion with partial derivatives for functions of several variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Saulius Norvidas","submitted_at":"2019-08-16T18:03:45Z","abstract_excerpt":"Let $B^p_{\\sigma}$, $1\\le p<\\infty$, $\\sigma>0$, denote the space of all $f\\in L^p(\\mathbb{R})$ such that the Fourier transform of $f$ (in the sense of distributions) vanishes outside $[-\\sigma,\\sigma]$. The classical sampling theorem states that each $f\\in B^p_{\\sigma}$ may be reconstructed exactly from its sample values at equispaced sampling points $\\{\\pi m/\\sigma\\}_{m\\in\\mathbb{Z}} $ spaced by $\\pi /\\sigma$. Reconstruction is also possible from sample values at sampling points $\\{\\pi \\theta m/\\sigma\\}_m $ with certain $1< \\theta\\le 2$ if we know $f(\\theta\\pi m/\\sigma) $ and $f'(\\theta\\pi m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07351","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.07351/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}