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Prescribing inner parts of derivatives of inner functions

Ivrii, Oleg (2019) Prescribing inner parts of derivatives of inner functions. Journal d'Analyse Mathématique, 139 (2). pp. 495-519. ISSN 0021-7670. doi:10.1007/s11854-019-0064-0.

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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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Additional Information:© 2019 The Hebrew University of Jerusalem. Received 01 February 2017; Revised 30 November 2018; First Online 05 November 2019.
Issue or Number:2
Record Number:CaltechAUTHORS:20191105-101645471
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Official Citation:Ivrii, O. Prescribing inner parts of derivatives of inner functions. JAMA 139, 495–519 (2019) doi:10.1007/s11854-019-0064-0
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99668
Deposited By: Tony Diaz
Deposited On:05 Nov 2019 18:22
Last Modified:16 Nov 2021 17:48

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