The Derivative of a Blaschke Product

  • Javad Mashreghi
Chapter
First Online:
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.
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Javad Mashreghi
    • 1
  1. 1.Département de mathématiques et de statistiqueUniversité LavalQuébecCanada

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