{"paper":{"title":"Cyclicity in reproducing kernel Hilbert spaces of analytic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Daniel Seco, Emmanuel Fricain, Javad Mashreghi","submitted_at":"2013-12-30T15:30:25Z","abstract_excerpt":"We introduce a large family of reproducing kernel Hilbert spaces $\\mathcal{H} \\subset \\mbox{Hol}(\\mathbb{D})$, which include the classical Dirichlet-type spaces $\\mathcal{D}_\\alpha$, by requiring normalized monomials to form a Riesz basis for $\\mathcal{H}$. Then, after precisely evaluating the $n$-th optimal norm and the $n$-th approximant of $f(z)=1-z$, we completely characterize the cyclicity of functions in $\\mbox{Hol}(\\overline{\\mathbb{D}})$ with respect to the forward shift."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7739","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"}