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Prescribing inner parts of derivatives of inner functions

  • Oleg IvriiEmail author
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Abstract

Let be the set of inner functions whose derivative lies in the Nevanlinna class. We show that up to a post-composition with a Möbius transformation, an inner function F ∈ ℐ is uniquely determined by the inner part of its derivative. We also characterize inner functions which can be represented as Inn F′ for some F ∈ ℐ in terms of the associated singular measure, namely, it must live on a countable union of Beurling–Carleson sets. This answers a question raised by K. Dyakonov.

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© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  1. 1.Department of MathematicsCalifornia Institute of TechnologyPasadenaUSA

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