The polynomial hull of unions of convex sets in $ℂ^n$

Tom 70 / 1996

Ulf Backlund, Anders Fällström Colloquium Mathematicum 70 (1996), 7-11 DOI: 10.4064/cm-70-1-7-11


We prove that three pairwise disjoint, convex sets can be found, all congruent to a set of the form ${(z_1,z_2,z_3) ∈ ℂ^3: |z_1|^2 + |z_2|^2 + |z_3|^{2m} ≤ 1}$, such that their union has a non-trivial polynomial convex hull. This shows that not all holomorphic functions on the interior of the union can be approximated by polynomials in the open-closed topology.


  • Ulf Backlund
  • Anders Fällström

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