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Domains with finite dimensional Bergman space. (English) Zbl 0534.32001
We give examples of Reinhardt domains in \({\mathbb{C}}^ 2\) with Bergman space of arbitrary finite dimension. The construction is easily extended to domains in \({\mathbb{C}}^ n\) with \(n\geq 3\). However, we show that for domains in \({\mathbb{C}}\) the dimension of the Bergman space is 0 or \(\infty\).

32A07 Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)
30H05 Spaces of bounded analytic functions of one complex variable
32F45 Invariant metrics and pseudodistances in several complex variables
32A35 \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables
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