{"paper":{"title":"Holomorphic functions on the symmetrized bidisk - realization, interpolation and extension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Haripada Sau, Tirthankar Bhattacharyya","submitted_at":"2015-11-29T03:51:24Z","abstract_excerpt":"There are three new things in this paper about the open symmetrized bidisk $\\mathbb G = \\{(z_1+z_2, z_1z_2) : |z_1|, |z_2| < 1\\}$. They are motivated in the Introduction. In this Abstract, we mention them in the order in which they will be proved.\n  \\begin{enumerate}\n\\item The Realization Theorem: A realization formula is demonstrated for every $f$ in the norm unit ball of $H^\\infty(\\mathbb G)$. \n\\item The Interpolation Theorem: Nevanlinna-Pick interpolation theorem is proved for data from the symmetrized bidisk and a specific formula is obtained for the interpolating function.\n\\item The Exten"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08962","kind":"arxiv","version":5},"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"}