Solving the Gleason problem on linearly convex domains
O Lemmers, J Wiegerinck - Mathematische Zeitschrift, 2002 - Springer
Mathematische Zeitschrift, 2002•Springer
… Backlund and Fällström showed ([5]) that there exists an H∞ -domain of holomorphy on
which the Gleason problem is not solvable. In this paper, we return to the original method of
Leibenzon, and use it to solve the Gleason problem for both A(Ω) and H∞(Ω) on C-convex
domains (these are domains such that their intersection with any complex line passing
through the domain is connected and simply connected) in Cn with C1+ϵ boundary. After
translation we can assume that the domain contains the origin, and that the point where we …
which the Gleason problem is not solvable. In this paper, we return to the original method of
Leibenzon, and use it to solve the Gleason problem for both A(Ω) and H∞(Ω) on C-convex
domains (these are domains such that their intersection with any complex line passing
through the domain is connected and simply connected) in Cn with C1+ϵ boundary. After
translation we can assume that the domain contains the origin, and that the point where we …
Abstract
Let be a bounded, connected linearly convex set in with boundary. We show that the maximal ideal (both in ) and ) consisting of all functions vanishing at is generated by the coordinate functions .
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