{"paper":{"title":"Remarks on one-component inner functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Atte Reijonen","submitted_at":"2018-05-13T12:09:39Z","abstract_excerpt":"A one-component inner function $\\Theta$ is an inner function whose level set\n  $$\\Omega_{\\Theta}(\\varepsilon)=\\{z\\in \\mathbb{D}:|\\Theta(z)|<\\varepsilon\\}$$ is connected for some $\\varepsilon\\in (0,1)$. We give a sufficient condition for a Blaschke product with zeros in a Stolz domain to be a one-component inner function. Moreover, a sufficient condition is obtained in the case of atomic singular inner functions.\n  We study also derivatives of one-component inner functions in the Hardy and Bergman spaces. For instance, it is shown that, for $0<p<\\infty$, the derivative of a one-component inner "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04866","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":""},"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"}