{"paper":{"title":"Characterizations of Symmetrized Polydisc","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Jaydeb Sarkar, Sushil Gorai","submitted_at":"2015-03-11T17:31:03Z","abstract_excerpt":"Let $\\Gamma_n$, $n \\geq 2$, denote the symmetrized polydisc in $\\mathbb{C}^n$, and $\\Gamma_1$ be the closed unit disc in $\\mathbb{C}$. We provide some characterizations of elements in $\\Gamma_n$. In particular, an element $(s_1, \\ldots, s_{n-1}, p) \\in \\mathbb{C}^n$ is in $\\Gamma_n$ if and only if $s_j = \\beta_j + \\overline{\\beta_{n-j}} p$, $j = 1, \\ldots, n-1$, for some $(\\beta_1, \\ldots, \\beta_{n-1}) \\in \\Gamma_{n-1}$, and $|p| \\leq 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03473","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"}