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

Abstract

Inspired by a result by Szőke, 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 $D\subset {\mathbb{P}}^1$.

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

References in corpus (1)

• On a theorem of Wiegerinck