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arXiv · 2009.10785

On a theorem of Wiegerinck

Róbert Szőke
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Abstract

A theorem of Wiegerinck says that the Bergman space over any domain in $\mathbb C$ is either trivial or infinite dimensional. We generalize this theorem in the following form. Let E be a hermitian, holomorphic vector bundle over $\mathbb P^1$, the later equipped with a volume form and $D$ an arbitrary domain in $\mathbb P^1$. Then the space of holomorphic L2 sections of $E$ over $D$ is either equal to $H^0(M,E)$ or it has infinite dimension.

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Róbert Szőke. 2020-09-22. On a theorem of Wiegerinck. https://doi.org/10.1007/s10476-022-0137-7

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