Definition
A sequence of points inside the unit disk is said to satisfy the Blaschke condition when
Given a sequence obeying the Blaschke condition, the Blaschke product is defined as
with factors
provided a ≠ 0. Here a* is the complex conjugate of a. When a = 0 take B(0,z) = z.
The Blaschke product B(z) defines a function analytic in the open unit disc, and zero exactly at the an (with multiplicity counted): furthermore it is in the Hardy class .
The sequence of an satisfying the convergence criterion above is sometimes called a Blaschke sequence.
Read more about this topic: Blaschke Product
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