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- W3188842590 abstract "In this paper, we consider the sum of weighted composition operator $C_{psi_{0},varphi_{0}}$ and the weighted composition--differentiation operator $D_{psi_{n},varphi_{n},n}$ on the Hardy and weighted Bergman spaces. We describe the spectrum of a compact operator $C_{psi_{0},varphi_{0}}+D_{psi_{n},varphi_{n},n}$ when the fixed point $w$ of $varphi_{0}$ and $varphi_{n}$ is inside the open unit disk and $psi_{n}$ has a zero at $w$ of order at least $n$. Also the lower estimate and the upper estimate on the norm of a weighted composition--differentiation operator on the Hardy space $H^{2}$ are obtained. Furthermore, we determine the norm of a composition--differentiation operator $D_{varphi,n}$, acting on the Hardy space $H^{2}$, in the case where $varphi(z)=bz$ for some complex number $b$ that $|b|<1$." @default.
- W3188842590 created "2021-08-16" @default.
- W3188842590 creator A5059594079 @default.
- W3188842590 date "2021-08-12" @default.
- W3188842590 modified "2023-09-27" @default.
- W3188842590 title "Weighted Composition--Differentiation Operator on the Hardy and Weighted Bergman Spaces." @default.
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