Reproducing kernel for a class of weighted Bergman spaces on the symmetrized polydisc

2011/06/20 by Gadadhar Misra, Misra, Gadadhar, Subrata Shyam Roy +3 · 3 citations
Mathematics · #47B32 #47B35 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1106.3868

openalex publication_date 2011/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A natural class of weighted Bergman spaces on the symmetrized polydisc is isometrically embedded as a subspace in the corresponding weighted Bergman space on the polydisc. We find an orthonormal basis for this subspace. It enables us to compute the kernel function for the weighted Bergman spaces on the symmetrized polydisc using the explicit nature of our embedding. This family of kernel functions include the Szegö and the Bergman kernel on the symmetrized polydisc.

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