{"paper":{"title":"An Analytic Model for Left-Invertible Weighted Shifts on Directed Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Sameer Chavan, Shailesh Trivedi","submitted_at":"2015-10-11T16:28:57Z","abstract_excerpt":"Let $\\mathscr T$ be a rooted directed tree with finite branching index $k_{\\mathscr T}$ and let $S_{\\lambda} \\in B(l^2(V))$ be a left-invertible weighted shift on ${\\mathscr T}$. We show that $S_{\\lambda}$ can be modelled as a multiplication operator $\\mathscr M_z$ on a reproducing kernel Hilbert space $\\mathscr H$ of $E$-valued holomorphic functions on a disc centered at the origin, where $E:=\\ker S^*_{\\lambda}$. The reproducing kernel associated with $\\mathscr H$ is multi-diagonal and of bandwidth $k_{\\mathscr T}.$ Moreover, $\\mathscr H$ admits an orthonormal basis consisting of polynomials "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03075","kind":"arxiv","version":2},"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"}