Derivatives of Inner Functions pp 99-124 | Cite as

The Derivative of a Blaschke Product

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• Javad Mashreghi

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First Online: 06 October 2012

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Part of the Fields Institute Monographs book series (FIM, volume 31)

Abstract

Let (z _n ) _{n ≥ 1} be a Blaschke sequence and let

$$B(z) = \prod \limits _{n=1}^{\infty }\frac{\vert {z}_{n}\vert } {{z}_{n}} \,\, \frac{{z}_{n} - z} {1 -\bar{ {z}}_{n}\,z}.$$

For a fixed point \(z \in \mathbb{D}\), we know that the partial products

$${B}_{N}(z) = \prod \limits _{n=1}^{N}\frac{\vert {z}_{n}\vert } {{z}_{n}} \,\, \frac{{z}_{n} - z} {1 -\bar{ {z}}_{n}\,z}$$

converge to B(z). Indeed, more is true.

Keywords

Blaschke Product Blaschke Sequence Radial Limit Angular Derivative Frostman 

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer Science+Business Media New York 2013

Authors and Affiliations

• Javad Mashreghi
  • 1

1. 1.Département de mathématiques et de statistiqueUniversité LavalQuébecCanada