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arXiv · 2110.02324

On the dimension of Bergman spaces on $\mathbb{P}^1$

Anne-Katrin Gallagher·Purvi Gupta·Liz Vivas
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Abstract

Inspired by a result by Sz\H{o}ke, we give potential-theoretic characterizations of the dimension of the Bergman space of holomorphic sections of a restriction of a holomorphic line bundle of $\mathbb{P}^1$ to some open set $D\subset\mathbb{P}^1$.

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Anne-Katrin Gallagher, Purvi Gupta, Liz Vivas. 2021-10-05. On the dimension of Bergman spaces on $\mathbb{P}^1$. https://doi.org/10.1007/s44007-022-00024-z

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