{"paper":{"title":"On filtered polynomial approximation on the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Heping Wang, Ian H. Sloan","submitted_at":"2015-09-13T01:23:25Z","abstract_excerpt":"This paper considers filtered polynomial approximations on the unit sphere $\\mathbb{S}^d\\subset \\mathbb{R}^{d+1}$, obtained by truncating smoothly the Fourier series of an integrable function $f$ with the help of a \"filter\" $h$, which is a real-valued continuous function on $[0,\\infty)$ such that $h(t)=1$ for $t\\in[0,1]$ and $h(t)=0$ for $t\\ge2$. The resulting \"filtered polynomial approximation\" (a spherical polynomial of degree $2L-1$) is then made fully discrete by approximating the inner product integrals by an $N$-point cubature rule of suitably high polynomial degree of precision, giving "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03792","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"}