2014/11/03 by Dror Varolin, Varolin, Dror
Mathematics · #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV
paper · pdf · doi:10.48550/arxiv.1411.0555
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
openalex publication_date 2014/11/03 · arxiv created 2015/08/10 · arxiv updated 2015/08/11 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
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.