User:Daviddaved/Blaschke products

< User:Daviddaved
Let a_i be a set of n points in the complex unit disc D. The corresponding Blaschke product is defined as

If the set of points is finite, the function defines the n-to-1 map of the unit disc onto itself,

f:\mathbb{D}\xrightarrow[]{n\leftrightarrow 1}\mathbb{D}.

If the set of points is infinite, the product converges and defines an automorphism of the complex unit disc, given the Blaschke condition

\sum_k (1-|a_k|) <\infty.

The following fact will be useful in our calculations: