User:DVD206/Blaschke products

From Wikibooks, open books for an open world
Jump to navigation Jump to search
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,

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

The following fact will be useful in our calculations: