Complex symmetric weighted composition operators on H γ ( D )
We study the complex symmetric structure of weighted composition operators of the form Wψ,ϕ on the Hilbert space Hγ(D) of holomorphic functions over the open unit disk D with reproducing kernels K(γ) w = (1 − wz)−γ, where γ ∈ N. First, we consider conjugations on Hγ(D) of the form Au,vf = u·f ◦ v...
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| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/107599 http://hdl.handle.net/10220/50352 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | We study the complex symmetric structure of weighted composition operators of
the form Wψ,ϕ on the Hilbert space Hγ(D) of holomorphic functions over the open
unit disk D with reproducing kernels K(γ) w = (1 − wz)−γ, where γ ∈ N. First, we
consider conjugations on Hγ(D) of the form Au,vf = u·f ◦ v (such conjugations are
also known as weighted composition conjugations) and characterize them into two
classes, denoted by C1 and C2. Then, we obtain explicit conditions for Wψ,ϕ when
it is C1-symmetric and C2-symmetric respectively |
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