Extensions of bounded holomorphic functions on the tridisk

• Łukasz Kosiński ^[1] ; John E. McCarthy ^[2]
  1. [1] Jagiellonian University

     Jagiellonian University

     Kraków, Polonia

     
  2. [2] Washington University in St. Louis

     Washington University in St. Louis

     Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 36, Nº 3, 2020, págs. 791-816
• Idioma: inglés
• DOI: 10.4171/rmi/1149
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• Resumen

  • A set V in the tridisk D3 has the polynomial extension property if for every polynomial p there is a function ϕ on D3 so that ∥ϕ∥D3=∥p∥V and ϕ|V=p|V. We study sets V that are relatively polynomially convex and have the polynomial extension property. If V is one-dimensional, and is either algebraic, or has polynomially convex projections, we show that it is a retract. If V is two-dimensional, we show that either it is a retract, or, for any choice of the coordinate functions, it is the graph of a function of two variables.