有限黎曼曲面上的Bergman插值。第一部分：渐近平坦情形
复变函数
2015-08-11 v3
摘要
我们研究通过从紧黎曼曲面移除有限个点所得到的开黎曼曲面的Bergman空间插值问题。我们为这样的曲面配备我们称之为渐近平坦共形度量的度量，即在一个紧子集外具有零曲率的完备度量。然后，我们建立了在渐近平坦黎曼曲面上的加权Bergman空间中插值的充要条件。
引用
@article{arxiv.1411.0555,
title = {Bergman interpolation on finite Riemann surfaces. Part I: Asymptotically Flat Case},
author = {Dror Varolin},
journal= {arXiv preprint arXiv:1411.0555},
year = {2015}
}
备注
The main result has been corrected: Sequences of density <1 are still interpolating, but the density of an interpolation sequence is only shown to be at most 1. The corrected result is sharp, by work of Borichev-Lyubarskii. Also added a motivating section on Shapiro-Shields interpolation. Otherwise typos and minor errors corrected. To appear in Journal d'Analyse