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Prescribing inner parts of derivatives of inner functions

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Abstract

Let ℐ 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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Authors and Affiliations

  1. Department of Mathematics, California Institute of Technology, 1200 E. California Boulevard, Pasadena, CA, 91125, USA

    Oleg Ivrii

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  1. Oleg Ivrii
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Correspondence to Oleg Ivrii.

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Ivrii, O. Prescribing inner parts of derivatives of inner functions. JAMA 139, 495–519 (2019). https://doi.org/10.1007/s11854-019-0064-0

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  • DOI: https://doi.org/10.1007/s11854-019-0064-0

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