Composition–differentiation operators on the Hardy space

Fatehi, Mahsa; Hammond, Christopher

doi:10.1090/proc/14898

Composition–differentiation operators on the Hardy space
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by Mahsa Fatehi and Christopher N. B. Hammond PDF

Proc. Amer. Math. Soc. 148 (2020), 2893-2900 Request permission

Abstract:

Let $\varphi$ be a nonconstant analytic self-map of the open unit disk in $\mathbb {C}$, with $\|\varphi \|_{\infty }<1$. Consider the operator $D_{\varphi }$, acting on the Hardy space $H^{2}$, given by differentiation followed by composition with $\varphi$. We obtain results relating to the adjoint, norm, and spectrum of such an operator.

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