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Composition-differentiation operators on S2(\mathbbD)

2022/08/08 by Robert F. Allen, Katherine Heller, Allen, Robert F. +3
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2208.03892

openalex publication_date 2022/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate composition-differentiation operators acting on the space S2, the space of analytic functions on the open unit disk whose first derivative is in H2. Specifically, we determine characterizations for bounded and compact composition-differentiation operators acting on Sp. In addition, for particular classes of inducing maps, we compute the norm, and identify the spectrum. Finally, for particular linear fractional inducing maps, we determine the adjoint of the composition-differentiation operator acting on weighted Bergman spaces which include S2, H2, and the Dirichlet space.

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