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Bull. Korean Math. Soc. 2023; 60(5): 1141-1154
Online first article August 31, 2023 Printed September 30, 2023
https://doi.org/10.4134/BKMS.b220215
Copyright © The Korean Mathematical Society.
Complex symmetric weighted composition-differentiation operators on $H^2$
Lian Hu, Songxiao Li, Rong Yang
Shantou University; Shantou University; University of Electronic Science and Technology of China
In this paper, we study the complex symmetric weighted composition-differentiation operator $D_{\psi,\phi}$ with respect to the conjugation $ JW_{\xi, \tau}$ on the Hardy space $H^2$. As an application, we characterize the necessary and sufficient conditions for such an operator to be normal under some mild conditions. Finally, the spectrum of $D_{\psi,\phi}$ is also investigated.
Keywords: Hardy space, weighted composition-differentiation operator, complex symmetric, spectrum
MSC numbers: Primary 30H10, 47B33
Supported by: This work was supported by Guangdong Basic and Applied Basic Research Foundation (nos. 2022A1515010317, 2023A1515010614).
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