{"paper":{"title":"Nonuniform sampling, reproducing kernels, and the associated Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","math.SP"],"primary_cat":"math.FA","authors_text":"Feng Tian, Palle Jorgensen","submitted_at":"2016-01-27T14:20:13Z","abstract_excerpt":"In a general context of positive definite kernels $k$, we develop tools and algorithms for sampling in reproducing kernel Hilbert space $\\mathscr{H}$ (RKHS). With reference to these RKHSs, our results allow inference from samples; more precisely, reconstruction of an \"entire\" (or global) signal, a function $f$ from $\\mathscr{H}$, via generalized interpolation of $f$ from partial information obtained from carefully chosen distributions of sample points. We give necessary and sufficient conditions for configurations of point-masses $\\delta_{x}$ of sample-points $x$ to have finite norm relative t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07380","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"}