Geodesic
The polynomial hull of unions of convex sets in $ℂ^n$
Colloquium Mathematicum, Tome 70 (1996) no. 1, pp. 7-11

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm-70-1-7-11

Ulf Backlund 1 ; Anders Fällström 1

1 
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Ulf Backlund; Anders Fällström. The polynomial hull of unions of convex sets in $ℂ^n$. Colloquium Mathematicum, Tome 70 (1996) no. 1, pp. 7-11. doi: 10.4064/cm-70-1-7-11

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