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

Ulf Backlund; Anders Fällström

ArticleOriginal scientific text

Title

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

Authors ¹, ¹

Affiliations

Department of Mathematics, Umeå University, S-901 87 Umeå, Sweden

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}) \in ℂ^{3} : {| z_{1} |}^{2} + {| z_{2} |}^{2} + {| z_{3} |}^{2 m} \leq 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.

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Title

The polynomial hull of unions of convex sets in ℂn

Affiliations

Abstract

Bibliography

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