{"paper":{"title":"Shannon Sampling and Parseval Frames on Compact Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.IT"],"primary_cat":"cs.IT","authors_text":"Isaac Z. Pesenson","submitted_at":"2013-12-06T15:08:00Z","abstract_excerpt":"Our article is a summary of some results for Riemannian manifolds that were obtained in \\cite{gpes}-\\cite{Pesssubm}. To the best of our knowledge these are the pioneering papers which contain the most general results about frames, Shannon sampling, and cubature formulas on compact and non-compact Riemannian manifolds. In particular, the paper \\cite{gpes} gives an \"end point\" construction of tight localized frames on homogeneous compact manifolds. The paper \\cite{Pessubm} is the first systematic development of localized frames on compact domains in Euclidean spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1882","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"}