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Complex symmetric weighted composition-differentiation operators. (English) Zbl 07683833

Summary: In this article, we mainly study the weighted composition-differentiation operator on the weighted Bergman space \(A^2_\alpha\) and the derivative Hardy space \(S^2_1\), which characterize complex symmetric weighted composition-differentiation operator \(D_{u, \varphi}\). Moreover, the normality and self-adjointness of \(D_{u, \varphi}\) are also discussed.

MSC:

47B91 Operators on complex function spaces
47B25 Linear symmetric and selfadjoint operators (unbounded)
47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
30H10 Hardy spaces
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
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