2024/05/06 by Gargi Ghosh, Ghosh, Gargi, Subrata Shyam Roy +1 · 1 citation
Mathematics · #30H10 #32A10 #47B35 #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2405.08002
openalex publication_date 2024/05/06 · openalex created_date 2024/05/16 · openalex updated_date 2026/07/30
Let Ω⊆\mathbb Cn be a bounded symmetric domain and f :Ω→ Ω^′⊆ \mathbb Cn be a proper holomorphic mapping which is factored by a finite complex reflection group G. We identify a family of reproducing kernel Hilbert spaces on Ω^′ arising naturally from the isotypic decomposition of the regular representation of G on the Hardy space H2(Ω). Each element of this family can be realized as a closed subspace of some L2-space on the Šilov boundary of Ω^′. The reproducing kernel Hilbert space associated to the sign representation of G is the Hardy space H2(Ω^′). We establish a Brown-Halmos type characterization for the Toeplitz operators on H2(Ω^′), where Ω^′ is the image of the open unit polydisc \mathbb Dn in \mathbb Cn under a proper holomorphic mapping factored by the finite complex reflection group G(m,p,n). Moreover, we prove various multiplicative properties of Toeplitz operators on H2(Ω^′), where Ω^′ is a proper holomorphic image of a bounded symmetric domain.