{"paper":{"title":"The Smirnov classes for the Fock space and complete Pick spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Michael T. Jury, Robert T.W. Martin","submitted_at":"2018-06-13T21:19:25Z","abstract_excerpt":"For a Hilbert function space $\\mathcal H$ the Smirnov class $\\mathcal N^+(\\mathcal H)$ is defined to be the set of functions expressible as a ratio of bounded multipliers of $\\mathcal H$, whose denominator is cyclic for the action of $Mult(\\mathcal H)$. It is known that for spaces $\\mathcal H$ with complete Nevanlinna-Pick (CNP) kernel, the inclusion $\\mathcal H\\subset \\mathcal N^+(\\mathcal H)$ holds. We give a new proof of this fact, which includes the new conclusion that every $h\\in\\mathcal H$ can be expressed as a ratio $b/a\\in\\mathcal N^+(\\mathcal H)$ with $1/a$ already belonging to $\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05270","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"}