Prime and Semiprime Inner Functions
This paper studies the structure of inner functions under the operation of composition, and in particular the notions or primeness and semiprimeness. Results proved include the density of prime finite Blaschke products in the set of finite Blaschke products, the semiprimeness of finite products of thin Blaschke products and their approximability by prime Blaschke products. An example of a nonsemiprime Blaschke product that is a Frostman Blaschke product is also provided.
Journal of the London Mathematical Society--Second Series
Chalendar, Isabelle; Gorkin, Pamela; and Partington, Jonathan R.. "Prime and Semiprime Inner Functions." Journal of the London Mathematical Society--Second Series (2013) : 779-800.