Bergman interpolation on finite Riemann surfaces. Part I: Asymptotically Flat Case

Autor:	Varolin, Dror
Rok vydání:	2014
Předmět:	Mathematics - Complex Variables
Druh dokumentu:	Working Paper
Popis:	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. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1411.0555 Zobrazit plný text záznamu View this record from Arxiv