Bergman interpolation on finite Riemann surfaces. Part I: Asymptotically Flat Case
Abstract
We study the Bergman space interpolation problem of open Riemann surfaces obtained from a compact Riemann surface by removing a finite number of points. We equip such a surface with what we call an asymptotically flat conformal metric, i.e., a complete metric with zero curvature outside a compact subset. We then establish necessary and sufficient conditions for interpolation in weighted Bergman spaces over asymptotically flat Riemann surfaces.
Keywords
Cite
@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}
}
Comments
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