{"paper":{"title":"Reproducing Kernel Hilbert Space vs. Frame Estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Myung-Sin Song, Palle E. T. Jorgensen","submitted_at":"2016-06-15T17:20:43Z","abstract_excerpt":"We consider conditions on a given system $\\mathcal{F}$ of vectors in Hilbert space $\\mathcal{H}$, forming a frame, which turn $\\mathcal{H}$ into a reproducing kernel Hilbert space. It is assumed that the vectors in $\\mathcal{F}$ are functions on some set $\\Omega$. We then identify conditions on these functions which automatically give $\\mathcal{H}$ the structure of a reproducing kernel Hilbert space of functions on $\\Omega$. We further give an explicit formula for the kernel, and for the corresponding isometric isomorphism. Applications are given to Hilbert spaces associated to families of Gau"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04868","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"}