{"paper":{"title":"Wandering subspaces of the Bergman space and the Dirichlet space over polydisc","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Chattopadhyay, B. Krishna Das, Jaydeb Sarkar, S. Sarkar","submitted_at":"2013-06-04T10:27:24Z","abstract_excerpt":"Doubly commutativity of invariant subspaces of the Bergman space and the Dirichlet space over the unit polydisc $\\mathbb{D}^n$ (with $ n \\geq 2$) is investigated. We show that for any non-empty subset $\\alpha=\\{\\alpha_1,\\dots,\\alpha_k\\}$ of $\\{1,\\dots,n\\}$ and doubly commuting invariant subspace $\\s$ of the Bergman space or the Dirichlet space over $\\D^n$, the tuple consists of restrictions of co-ordinate multiplication operators $M_{\\alpha}|_\\s:=(M_{z_{\\alpha_1}}|_\\s,\\dots, M_{z_{\\alpha_k}}|_\\s)$ always possesses wandering subspace of the form \\[\\bigcap_{i=1}^k(\\s\\ominus z_{\\alpha_i}\\s). \\]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0724","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"}