{"paper":{"title":"A Solution to Schroeder's Equation in Several Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Robert A. Bridges","submitted_at":"2011-06-16T23:38:29Z","abstract_excerpt":"Let \\phi be a self-map of B^n, the unit ball in C^n, fixing 0, and having full-rank at 0. If \\phi (0)= 0, Koenigs proved in 1884 that in the well- known case n = 1, Schroeder's equation, f \\circ \\phi = \\phi '(0) f has a solution f, which is bijective near 0 precisely when \\phi '(0) \\neq 0. In 2003, Cowen and MacCluer formulated the analogous problem in C^n (for a non-negative integer n) by defining Schroeder's equation in several variables as F \\circ \\phi = \\phi '(0)F and giving appropriate assumptions on \\phi . The 2003 Cowen and MacCluer paper also provides necessary and sufficient condition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3370","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"}