2023/09/21 by Gargi Ghosh, E.K. Narayanan · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Holomorphic and Operator Theory
paper · doi:10.1016/j.bulsci.2023.103340
openalex publication_date 2023/09/21 · crossref created 2023/09/21 · crossref issued 2023/11/01 · crossref published 2023/11/01 · crossref published-print 2023/11/01 · crossref deposited 2025/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31 · crossref indexed 2026/07/31
Let G be a finite pseudoreflection group and be a bounded domain which is a G -space. We establish identities involving Toeplitz operators on the weighted Bergman spaces of Ω and using invariant theory and representation theory of G . This, in turn, provides techniques to study algebraic properties of Toeplitz operators on the weighted Bergman space on . We specialize on the generalized zero-product problem and characterization of commuting pairs of Toeplitz operators. As a consequence, more intricate results on Toeplitz operators on the weighted Bergman spaces on some specific quotient domains (namely symmetrized polydisc, monomial polyhedron, Rudin's domain) have been obtained.