Iterative Variable-Blaschke Factorization

Abstract

Blaschke factorization allows us to write any holomorphic function F as a formal serieswhere a i ∈ C and B i is a Blaschke product. We introduce a more general variation of the canonical Blaschke product and study the resulting formal series. We prove that the series converges exponentially in the Dirichlet space given a suitable choice of parameters if F is a polynomial and we provide explicit conditions under which this convergence can occur. Finally, we derive analogous properties of Blaschke factorization using our new variable framework.2010 Mathematics Subject Classification. 30A10, 30B50.