{"paper":{"title":"Kernel Approximation on Manifolds II: The $L_{\\infty}$-norm of the $L_2$-projector","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.NA"],"primary_cat":"math.CA","authors_text":"Fran J Narcowich, Joe D Ward, Thomas Hangelbroek, Xingping Sun","submitted_at":"2010-05-13T21:13:20Z","abstract_excerpt":"This article addresses two topics of significant mathematical and practical interest in the theory of kernel approximation: the existence of local and stable bases and the L_p--boundedness of the least squares operator. The latter is an analogue of the classical problem in univariate spline theory, known there as the \"de Boor conjecture\". A corollary of this work is that for appropriate kernels the least squares projector provides universal near-best approximations for functions f\\in L_p, 1\\le p\\le \\infty."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2424","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"}