{"paper":{"title":"Weighted estimates for the discrete Laplacian on the cubic lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Evgeny L. Korotyaev, Jacob Schach M{\\o}ller","submitted_at":"2017-01-13T09:32:28Z","abstract_excerpt":"We consider the discrete Laplacian $\\Delta$ on the cubic lattice $\\mathbb Z^d$, and deduce estimates on the group $e^{it\\Delta}$ and the resolvent $(\\Delta-z)^{-1}$, weighted by $\\ell^q(\\mathbb Z^d)$-weights for suitable $q\\geq 2$. We apply the obtained results to discrete Schr\\\"odinger operators in dimension $d\\geq 3$ with potentials from $\\ell^p(\\mathbb Z^d)$ with suitable $p\\geq 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03605","kind":"arxiv","version":2},"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"}