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arXiv · 2004.00854

Multiplication operator on the Bergman space by a proper holomorphic map

Gargi Ghosh
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Abstract

Suppose that $f := (f_1,\ldots,f_d):\Omega_1\to\Omega_2$ is a proper holomorphic map between two bounded domains in $\mathbb C^d.$ In this paper, we find a non-trivial minimal joint reducing subspace for the multiplication operator (tuple) $M_f=(M_{f_1},\ldots, M_{f_d})$ on the Bergman space $\mathbb A^2(\Omega_1)$, say $\mathcal M.$ We further show that the restriction of $(M_{f_1},\ldots,M_{f_d})$ to $\mathcal M$ is unitarily equivalent to Bergman operator on $\mathbb A^2(\Omega_2).$

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Gargi Ghosh. 2020-04-02. Multiplication operator on the Bergman space by a proper holomorphic map. https://arxiv.org/abs/2004.00854

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