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arXiv · 2505.21346

A Burns-Krantz type theorem for Blaschke products

Annika Moucha
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Abstract

Let $f$ be a holomorphic function mapping the open unit disk into itself. We establish a boundary version of Schwarz' lemma in the spirit of a result by Burns and Krantz and provide sufficient conditions on the local behaviour of $f$ near some boundary point that forces $f$ to be a Blaschke product with predescribed critical points. For the proof, a local Julia type inequality based on Nehari's sharpening of Schwarz' lemma is established.

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Annika Moucha. 2025-05-27. A Burns-Krantz type theorem for Blaschke products. https://doi.org/10.1090/proc%2F17265

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