The polynomial hull of unions of convex sets in $ℂ^n$
Volume 70 / 1996
Colloquium Mathematicum 70 (1996), 7-11
DOI: 10.4064/cm-70-1-7-11
Abstract
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.
