{"paper":{"title":"Shift operators, Cauchy integrals and approximations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bartosz Malman","submitted_at":"2023-08-12T07:56:37Z","abstract_excerpt":"This article consists of two connected parts. In the first part, we study the shift invariant subspaces in certain $\\mathcal{P}^2(\\mu)$-spaces, which are the closures of analytic polynomials in the Lebesgue spaces $\\mathcal{L}^2(\\mu)$ defined by a class of measures $\\mu$ living on the closed unit disk $\\overline{\\mathbb{D}}$. The measures $\\mu$ which occur in our study have a part on the open disk $\\mathbb{D}$ which is radial and decreases at least exponentially fast near the boundary. Our focus is on those shift invariant subspaces which are generated by a bounded function in $H^\\infty$. In t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.06495","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.06495/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}