{"paper":{"title":"Landau's theorem for slice regular functions on the quaternionic unit ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Caterina Stoppato, Cinzia Bisi","submitted_at":"2017-01-27T16:48:49Z","abstract_excerpt":"Along with the development of the theory of slice regular functions over the real algebra of quaternions $\\mathbb{H}$ during the last decade, some natural questions arose about slice regular functions on the open unit ball $\\mathbb{B}$ in $\\mathbb{H}$. This work establishes several new results in this context. Along with some useful estimates for slice regular self-maps of $\\mathbb{B}$ fixing the origin, it establishes two variants of the quaternionic Schwarz-Pick lemma, specialized to maps $\\mathbb{B}\\to\\mathbb{B}$ that are not injective. These results allow a full generalization to quaternio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08112","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"}