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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 $$\infty$$.

##### MSC:
 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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##### References:
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