Blaschke product

Summary

A Blaschke product is a bounded holomorphic function on the unit disc built as a product of disc automorphisms, one for each prescribed zero. It exists exactly when the zeros satisfy the Blaschke condition $\sum_n (1 - \abs{a_n}) < \infty$. Blaschke products are the basic inner functions, and every nonzero function in a Hardy space factors through the Blaschke product of its zeros.