{"paper":{"title":"Classification of Drury-Arveson-type Hilbert modules associated with certain directed graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Deepak Kumar Pradhan, Sameer Chavan, Shailesh Trivedi","submitted_at":"2017-09-09T06:56:41Z","abstract_excerpt":"Given a directed Cartesian product $\\mathscr T$ of locally finite, leafless, rooted directed trees $\\mathscr T_1, \\ldots, \\mathscr T_d$ of finite joint branching index, one may associate with $\\mathscr T$ the Drury-Arveson-type $\\mathbb C[z_1, \\ldots, z_d]$-Hilbert module $\\mathscr H_{\\mathfrak c_a}(\\mathscr T)$ of vector-valued holomorphic functions on the open unit ball $\\mathbb B^d$ in $\\mathbb C^d$, where $a >0.$ In case all directed trees under consideration are without branching vertices, $\\mathscr H_{\\mathfrak c_a}(\\mathscr T)$ turns out to be the classical Drury-Arveson-type Hilbert mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02922","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"}