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

100%

Backlund U., Fällström A.

Colloquium Mathematicum

1996

tom 70

nr 1

7-11

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.

Spectrum of certain Banach algebras and ∂̅-problems

81%

Carlsson L., Cegrell U., Fällström A.

Annales Polonici Mathematici

2007

tom 90

nr 1

51-58

We study the spectrum of certain Banach algebras of holomorphic functions defined on a domain Ω where ∂̅-problems with certain estimates can be solved. We show that the projection of the spectrum onto ℂⁿ equals Ω̅ and that the fibers over Ω are trivial. This is used to solve a corona problem in the special case where all but one generator are continuous up to the boundary.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Colloquium Mathematicum

2 Fällström A.

1 Backlund U.

1 Carlsson L.

1 Cegrell U.

1 2007

1 1996

Wyniki wyszukiwania

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

Spectrum of certain Banach algebras and ∂̅-problems