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 
@article{10_4064_cm_70_1_7_11,
     author = {Ulf Backlund and Anders F\"allstr\"om},
     title = {The polynomial hull of unions of convex sets in $\ensuremath{\mathbb{C}}^n$},
     journal = {Colloquium Mathematicum},
     pages = {7--11},
     publisher = {mathdoc},
     volume = {70},
     number = {1},
     year = {1996},
     doi = {10.4064/cm-70-1-7-11},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-70-1-7-11/}
}
TY  - JOUR
AU  - Ulf Backlund
AU  - Anders Fällström
TI  - The polynomial hull of unions of convex sets in $ℂ^n$
JO  - Colloquium Mathematicum
PY  - 1996
SP  - 7
EP  - 11
VL  - 70
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm-70-1-7-11/
DO  - 10.4064/cm-70-1-7-11
LA  - en
ID  - 10_4064_cm_70_1_7_11
ER  - 
%0 Journal Article
%A Ulf Backlund
%A Anders Fällström
%T The polynomial hull of unions of convex sets in $ℂ^n$
%J Colloquium Mathematicum
%D 1996
%P 7-11
%V 70
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm-70-1-7-11/
%R 10.4064/cm-70-1-7-11
%G en
%F 10_4064_cm_70_1_7_11
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. http://geodesic.mathdoc.fr/articles/10.4064/cm-70-1-7-11/

Cité par Sources :