{"paper":{"title":"Thinplate Splines on the Sphere","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Rick K. Beatson, Wolfgang zu Castell","submitted_at":"2018-01-04T11:43:18Z","abstract_excerpt":"In this paper we give explicit closed forms for the semi-reproducing kernels associated with thinplate spline interpolation on the sphere. Polyharmonic or thinplate splines for ${\\mathbb R}^d$ were introduced by Duchon and have become a widely used tool in myriad applications. The analogues for ${\\mathbb S}^{d-1}$ are the thin plate splines for the sphere. The topic was first discussed by Wahba in the early 1980's, for the ${\\mathbb S}^2$ case. Wahba presented the associated semi-reproducing kernels as infinite series. These semi-reproducing kernels play a central role in expressions for the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01313","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"}