{"paper":{"title":"Cardinal Interpolation With General Multiquadrics: Convergence Rates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jeff Ledford, Keaton Hamm","submitted_at":"2015-06-04T18:18:28Z","abstract_excerpt":"This article pertains to interpolation of Sobolev functions at shrinking lattices $h\\mathbb{Z}^d$ from $L_p$ shift-invariant spaces associated with cardinal functions related to general multiquadrics, $\\phi_{\\alpha,c}(x):=(|x|^2+c^2)^\\alpha$. The relation between the shift-invariant spaces generated by the cardinal functions and those generated by the multiquadrics themselves is considered. Additionally, $L_p$ error estimates in terms of the dilation $h$ are considered for the associated cardinal interpolation scheme. This analysis expands the range of $\\alpha$ values which were previously kno"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07387","kind":"arxiv","version":4},"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"}