Fine Boundary Behavior and Invariant Subspaces of Harmonically Weighted Dirichlet Spaces

被引：0
作者：
Dominique Guillot
机构：
[1] Pavillon Alexandre-Vachon,Département de mathématiques et de statistique
[2] Université Laval,undefined
来源：
Complex Analysis and Operator Theory | 2012年 / 6卷
关键词：
Weighted Dirichlet spaces; Dirichlet space; Radial limits; Invariant subspaces; Logarithmic capacity; Primary 46E22; Secondary 47B32;
D O I：
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学科分类号：
摘要：
We study the boundary behavior of functions in spaces of Dirichlet-type by using non-linear capacities generalizing the logarithmic capacity. We use these capacities to obtain information about the invariant subspaces of the shift operator. As an application, we prove an analogue of a conjecture of Brown and Shields when the space is weighted by the Poisson integral of a finite sum of atoms.
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页码：1211 / 1230
页数：19
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