Maximal Blaschke Products

Daniela Kraus; Oliver Roth

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arXiv · 1303.6769

Maximal Blaschke Products

Daniela Kraus·Oliver Roth

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Abstract

We consider the classical problem of maximizing the derivative at a fixed point over the set of all bounded analytic functions in the unit disk with prescribed critical points. We show that the extremal function is essentially unique and always an indestructible Blaschke product. This result extends the Nehari--Schwarz Lemma and leads to a new class of Blaschke products called maximal Blaschke products. We establish a number of properties of maximal Blaschke products, which indicate that maximal Blaschke products constitute an appropriate infinite generalization of the class of finite Blaschke products.

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BibTeX RIS

Daniela Kraus, Oliver Roth. 2013-03-27. Maximal Blaschke Products. https://arxiv.org/abs/1303.6769

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