{"paper":{"title":"Finite Blaschke products and the construction of rational $\\Gamma$-inner functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Jim Agler, N. J. Young, Zinaida A. Lykova","submitted_at":"2015-05-10T17:56:38Z","abstract_excerpt":"Let \\[ \\Gamma = \\{(z+w, zw): |z|\\leq 1, |w|\\leq 1\\} \\subset \\mathbb{C}^2. \\] A $\\Gamma$-inner function is defined to be a holomorphic map $h$ from the unit disc $\\mathbb{D}$ to $\\Gamma$ whose boundary values at almost all points of the unit circle $\\mathbb{T}$ belong to the distinguished boundary $b\\Gamma$ of $\\Gamma$. A rational $\\Gamma$-inner function $h$ induces a continuous map $h|_\\mathbb{T}$ from the unit circle to $b\\Gamma$. The latter set is topologically a M\\\"obius band and so has fundamental group $\\mathbb{Z}$. The {\\em degree} of $h$ is defined to be the topological degree of $h|_\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02415","kind":"arxiv","version":3},"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"}