Interpolating Blaschke Products and Angular Derivatives
Transactions of the American Mathematical Society
We show that to each inner function, there corresponds at least one interpolating Blaschke product whose angular derivatives have precisely the same behavior as the given inner function. We characterize the Blaschke products invertible in the closed algebra generated by the algebra of bounded analytic functions and the conjugates of Blaschke products with angular derivative finite everywhere. We study the most well-known example of a Blaschke product with infinite angular derivative everywhere and show that it is an interpolating Blaschke product. We conclude the paper with a method for constructing thin Blaschke products with infinite angular derivative everywhere.
Gorkin, Pamela and Gallardo Gutierrez, Eva A.. "Interpolating Blaschke Products and Angular Derivatives." Transactions of the American Mathematical Society 364, no. 5 (2012) : 2319-2337.