{"paper":{"title":"Dilation and Functional Models for Pure $\\mathbf{\\Theta}_n$-Contractions and the von Neumann Inequality on Distinguished Varieties in $\\mathbf{\\Theta}_n$","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Aparna Gupta, Bhaskar Paul, Shubhankar Mandal Avijit Pal","submitted_at":"2026-08-13T15:31:14Z","abstract_excerpt":"In this paper, we introduce the notion of a distinguished variety in the domain $\\mathbf{\\Theta}_n$. One of the main results of the paper is a determinantal representation for every distinguished variety in $\\mathbf{\\Theta}_n$. We also show that the closure of every distinguished variety is polynomially convex. Furthermore, we obtain a dilation and a functional model for a class of pure $\\mathbf{\\Theta}_n$-contractions. Finally, we show that for a $\\mathbf{\\Theta}_n$-contraction $\\mathbf{T}=(T_1,\\dots,T_n)$ such that $T_n^*$ is a pure contraction, there exists an algebraic variety in $\\mathbf{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.13366","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.13366/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}