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arXiv · 2207.09015

Composition-differentiation operators on the Dirichlet space

Robert F. Allen·Katherine Heller·Matthew A. Pons
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Abstract

We investigate composition-differentiation operators acting on the Dirichlet space of the unit disk. Specifically, we determine characterizations for bounded, compact, and Hilbert-Schmidt composition-differentiation operators. In addition, for particular classes of inducing maps, we derive an adjoint formula, compute the norm, and identify the spectrum.

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Robert F. Allen, Katherine Heller, Matthew A. Pons. 2022-07-19. Composition-differentiation operators on the Dirichlet space. https://doi.org/10.1016/j.jmaa.2022.126186

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