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 H-infinity[(b) over bar : b has finite angular derivative 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.
Transactions of the American Mathematical Society
First published in Transactions of the American Mathematical Society in Vol. 364, No. 5 (May 2012), published by the American Mathematical Society
Gallardo-Gutierrez, Eva A. and Gorkin, Pamela. "INTERPOLATING BLASCHKE PRODUCTS AND ANGULAR DERIVATIVES." Transactions of the American Mathematical Society (2012) : 2319-2337.