Geodesic
The polynomial hull of unions of convex sets in $ℂ^n$
Colloquium Mathematicum, Tome 70 (1996) no. 1, pp. 7-11
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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. 
@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},
     year = {1996},
     volume = {70},
     number = {1},
     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
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
%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

Cité par Sources :