A Burns-Krantz type theorem for Blaschke products
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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