Blaschke product


Suppose that {an} is a sequence of complex numbersPlanetmathPlanetmath with 0<|an|<1 and n=1(1-|an|)<, then


is called the Blaschke productMathworldPlanetmath.

This product converges uniformly on compact subsets of the unit disc, and thus B is a holomorhic function on the unit disc. Further it is the function on the disc that has zeros exactly at {an}. And finally for z in the unit disc, |B(z)|1.


Sometimes Ba(z):=z-a1-a¯z is called the Blaschke factor.

With this definition, the Blascke product becomes B(z)=n=1|an|anBan(z).


  • 1 John B. Conway. . Springer-Verlag, New York, New York, 1978.
  • 2 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
Title Blaschke product
Canonical name BlaschkeProduct
Date of creation 2013-03-22 14:19:35
Last modified on 2013-03-22 14:19:35
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 8
Author jirka (4157)
Entry type Definition
Classification msc 30C45
Defines Blascke factor