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Weighted Composition-differentiation Operators on the Bergman Space
Complex Analysis and Operator Theory ( IF 0.7 ) Pub Date : 2021-06-17 , DOI: 10.1007/s11785-021-01116-4
Kaikai Han , Maofa Wang

In this paper, we study weighted composition-differentiation operators of the form \(D_{n,\varphi , \psi }\) on the Bergman space \(A^{2}\). We obtain explicit conditions for \(D_{n,\varphi , \psi }\) when it is complex symmetric with respect to conjugations \({\mathcal {C}}_{1}\) and \({\mathcal {C}}_{2}\) respectively. In addition, invariant subspaces of composition-differentiation operators are considered. Finally, we give spectral properties of weighted composition-differentiation operators.



中文翻译:

Bergman 空间上的加权组合微分算子

在本文中,我们研究了 Bergman 空间\(A^{2}\)上形式为\(D_{n,\varphi , \psi }\) 的加权组合微分算子。当\(D_{n,\varphi , \psi }\)关于共轭\({\mathcal {C}}_{1}\)\({\mathcal { C}}_{2}\)分别。此外,还考虑了组合微分算子的不变子空间。最后,我们给出了加权成分微分算子的谱特性。

更新日期:2021-06-18
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