{"paper":{"title":"Rational inner functions on a square-matrix polyball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Anatolii Grinshpan, Dmitry S. Kaliuzhnyi-Verbovetskyi, Hugo J. Woerdeman, Victor Vinnikov","submitted_at":"2015-05-20T16:05:13Z","abstract_excerpt":"We establish the existence of a finite-dimensional unitary realization for every matrix-valued rational inner function from the Schur--Agler class on a unit square-matrix polyball. In the scalar-valued case, we characterize the denominators of these functions. We also show that every polynomial with no zeros in the closed domain is such a denominator. One of our tools is the Kor\\'{a}nyi--Vagi theorem generalizing Rudin's description of rational inner functions to the case of bounded symmetric domains; we provide a short elementary proof of this theorem suitable in our setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05437","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"}