Mathematische Zeitschrift

, Volume 240, Issue 4, pp 823–834

Solving the Gleason problem on linearly convex domains

  • Oscar Lemmers
  • Jan Wiegerinck
Original article

DOI: 10.1007/s002090100400

Cite this article as:
Lemmers, O. & Wiegerinck, J. Math Z (2002) 240: 823. doi:10.1007/s002090100400


Let \(\Omega\) be a bounded, connected linearly convex set in \({\mathbf{C}} ^n\) with \(C^{1+\epsilon}\) boundary. We show that the maximal ideal (both in \(H^{\infty}(\Omega)\)) and \(A^{m}(\Omega), 0 \leq m \leq \infty\)) consisting of all functions vanishing at \(p \in \Omega\) is generated by the coordinate functions \(z_1 - p_1, \ldots, z_n - p_n\).

Mathematics Subject Classification (2000): 32A38, 32F17

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Oscar Lemmers
    • 1
  • Jan Wiegerinck
    • 1
  1. 1.Department of mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands (e-mail: {lemmers, janwieg} NL