{"paper":{"title":"Monomial basis in Korenblum type spaces of analytic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jari Taskinen, Jos\\'e Bonet, Wolfgang Lusky","submitted_at":"2017-12-01T11:33:17Z","abstract_excerpt":"It is shown that the monomials $\\Lambda=(z^n)_{n=0}^{\\infty}$ are a Schauder basis of the Fr\\'echet spaces $A_+^{-\\gamma}, \\ \\gamma \\geq 0,$ that consists of all the analytic functions $f$ on the unit disc such that $(1-|z|)^{\\mu}|f(z)|$ is bounded for all $\\mu > \\gamma$. Lusky \\cite{L} proved that $\\Lambda$ is not a Schauder basis for the closure of the polynomials in weighted Banach spaces of analytic functions of type $H^{\\infty}$. A sequence space representation of the Fr\\'echet space $A_+^{-\\gamma}$ is presented. The case of (LB)-spaces $A_{-}^{-\\gamma}, \\ \\gamma > 0,$ that are defined as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00280","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"}