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## Colloquium Mathematicum

1996 | 70 | 1 | 7-11
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
7-11
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-01-23
Twórcy
autor
• Department of Mathematics, Umeå University, S-901 87 Umeå, Sweden
autor
• Department of Mathematics, Umeå University, S-901 87 Umeå, Sweden
Bibliografia
• [BePi] E. Bedford and S. Pinchuk, Domains in $ℂ^n+1$ with noncompact automorphism group, J. Geom. Anal. 1 (1991), 165-192.
• [Kal] E. Kallin, Polynomial convexity: The three spheres problem, in: Proceedings of the Conference on Complex Analysis, Minneapolis 1964, H. Röhrl, A. Aeppli and E. Calabi (eds.), Springer, 1965, 301-304.
• [Khud] G. Khudaĭberganov, On polynomial and rational convexity of unions of compacts in $ℂ^n$, Izv. Vuz. Mat. 2 (1987), 70-74 (in Russian).
• [KyKh] A. M. Kytmanov and G. Khudaĭberganov, An example of a nonpolynomially convex compact set consisting of three non-intersecting ellipsoids, Sibirsk. Mat. Zh. 25 (5) (1984), 196-198 (in Russian).
• [Ros] J.-P. Rosay, The polynomial hull of non-connected tube domains, and an example of E. Kallin, Bull. London Math. Soc. 21 (1989), 73-78.
• [Wer1] J. Wermer, Polynomial approximation on an arc in $ℂ^3$, Ann. of Math. 62 (1955), 269-270.
• [Wer2] J. Wermer, An example concerning polynomial convexity, Math. Ann. 139 (1959), 147-150.
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