当前位置: X-MOL 学术Complex Anal. Oper. Theory › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Ergodic Properties of Composition Semigroups on the Disc Algebra
Complex Analysis and Operator Theory ( IF 0.8 ) Pub Date : 2021-04-01 , DOI: 10.1007/s11785-021-01105-7
Leonhard Frerick , Alberto Rodríguez-Arenas , Jochen Wengenroth

Every semigroup \(\{\varphi _t\}_{t\ge 0}\) of self-maps of the disc defines a semigroup \(\{C_{\varphi _t}\}_{t\ge 0}\) of compositions operators on the space of holomorphic functions on the disc. We characterize the (uniform) mean ergodicity (in the sense of continuous means) and the asymptotic behaviour of these operators when they define a \(C_0\)-semigroup on the disc algebra, in terms of the Denjoy–Wolff point and the associated planar domain in the sense of Berkson and Porta. Finally we deal with the case of Hardy and Bergman spaces.



中文翻译:

圆盘代数上的合成半群的遍历性质

光盘自映射的每个半群\(\ {\ varphi _t \} _ {t \ ge 0} \都定义了一个半群\(\ {C _ {\ varphi _t} \} _ {t \ ge 0} \ )在圆盘上全纯函数空间上的合成算子。当这些算子在圆盘代数上定义\(C_0 \)-半群时,我们用Denjoy-Wolff点和相关联的特征来描述(均匀)平均遍历性(就连续均值而言)和这些算子的渐近行为伯克森(Berkson)和波尔塔(Porta)的平面域。最后,我们处理Hardy和Bergman空间的情况。

更新日期:2021-04-02
down
wechat
bug