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

Anne-Katrin Gallagher; Purvi Gupta; Liz Vivas

doi:10.1007/s44007-022-00024-z

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

Complex Variables 2024-05-06 v2

Authors: 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 $D\subset\mathbb{P}^1$ .

Keywords

bergman space holomorphic line bundle projective line potential theory dimension

Cite

@article{arxiv.2110.02324,
  title  = {On the dimension of Bergman spaces on $\mathbb{P}^1$},
  author = {Anne-Katrin Gallagher and Purvi Gupta and Liz Vivas},
  journal= {arXiv preprint arXiv:2110.02324},
  year   = {2024}
}

Comments

18 pages; included a reference for Lemma 3.1 and simplified the proof of Lemma 3.1 following a suggestion of Pflug; fixed some typos

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

Abstract

Keywords

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