Hardy-Smirnov空间上的Hermitian复合算子

IF 0.3 Q4 MATHEMATICS Concrete Operators Pub Date : 2017-01-26 DOI:10.1515/conop-2017-0002

Gajath Gunatillake

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引用次数: 1

摘要

设Ω是复平面的开单连通真子集，φ是Ω的解析自映射。如果f在Ω上定义的Hardy-Smirnov空间中，则将f带到fºφ的算子是合成算子。我们证明了对于任何Ω，诱导有界埃尔米特合成算子的解析自映射的形式为Φ（w）=aw+b，其中a是实数。对于ceratinΩ，我们完全描述了a和b的值，它们诱导了有界埃尔米特复合算子。

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Hermitian composition operators on Hardy-Smirnov spaces

Abstract Let Ω be an open simply connected proper subset of the complex plane and φ an analytic self map of Ω. If f is in the Hardy-Smirnov space defined on Ω, then the operator that takes f to f º φ is a composition operator. We show that for any Ω, analytic self maps that induce bounded Hermitian composition operators are of the form Φ(w) = aw + b where a is a real number. For ceratin Ω, we completely describe values of a and b that induce bounded Hermitian composition operators.

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