{"paper":{"title":"Fractional discrete Laplacian versus discretized fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.NA"],"primary_cat":"math.AP","authors_text":"J. L. Torrea, J. L. Varona, L. Roncal, \\'O. Ciaurri, P. R. Stinga","submitted_at":"2015-07-17T14:34:04Z","abstract_excerpt":"We define and study some properties of the fractional powers of the discrete Laplacian $$(-\\Delta_h)^s,\\quad\\hbox{on}~\\mathbb{Z}_h = h\\mathbb{Z},$$ for $h>0$ and $0<s<1$. A comparison between our fractional discrete Laplacian and the \\textit{discretized} continuous fractional Laplacian as $h\\to0$ is carried out. We get estimates in $\\ell^\\infty$ for the error of the approximation in terms of $h$ under minimal regularity assumptions. Moreover, we provide a pointwise formula with an explicit kernel and deduce H\\\"older estimates for $(-\\Delta_h)^s$. A study of the negative powers (or discrete fra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04986","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"}