{"paper":{"title":"Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.OA"],"primary_cat":"math.FA","authors_text":"Caixing Gu, Jie Xiao, Shuaibing Luo","submitted_at":"2018-06-28T03:36:53Z","abstract_excerpt":"This paper is devoted to the study of reducing subspaces for multiplication operator $M_\\phi$ on the Dirichlet space with symbol of finite Blaschke product. The reducing subspaces of $M_\\phi$ on the Dirichlet space and Bergman space are related. Our strategy is to use local inverses and Riemann surface to study the reducing subspaces of $M_\\phi$ on the Bergman space, and we discover a new way to study the Riemann surface for $\\phi^{-1}\\circ\\phi$. By this means, we determine the reducing subspaces of $M_\\phi$ on the Dirichlet space when the order of $\\phi$ is $5$; $6$; $7$ and answer some quest"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10757","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"}