Reinhardt domains and the Gleason problem

• Oscar Lemmers ^[1] ; Jan Wiegerinck ^[1]
  1. [1] University of Amsterdam

     University of Amsterdam

     Países Bajos

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 30, Nº 2, 2001, págs. 405-414
• Idioma: inglés
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• Resumen

  • As usual, let be the uniform algebra consisting of the functions which are holomorphic on S2, and continuous on a, and let be the set of bounded holomorphic functions on SZ. Throughout this paper S2 will be a bounded Reinhardt domain in C~ with C2-boundary.

    We show that the maximal ideal (both in and consisting of functions vanishing at p E Q, is generated by the functions (z 1 - PI), (Z2 - P2 ) ~ at first for the case that Q is pseudoconvex, then without this condition.