{"paper":{"title":"Invertibility Threshold for Nevanlinna Quotient Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Artur Nicolau, Pascal J. Thomas","submitted_at":"2019-04-15T08:38:23Z","abstract_excerpt":"Let $\\mathcal{N}$ be the Nevanlinna class and let $B$ be a Blaschke product. It is shown that the natural invertibility criterion in the quotient algebra $\\mathcal{N} / B \\mathcal{N}$, that is, $|f| \\ge e^{-H} $ on the set $B^{-1}\\{0\\}$ for some positive harmonic function $H$, holds if and only if the function $- \\log |B|$ has a harmonic majorant on the set $\\{z\\in\\mathbb{D}:\\rho(z,\\Lambda)\\geq e^{-H(z)}\\}$; at least for large enough functions $H$. We also study the corresponding class of positive harmonic functions $H$ in the unit disc such that the latter condition holds. We also discuss the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06908","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"}