Factorization theory for stable, discrete-time inner functions

A factorization theory for stable, matrix valued inner functions in state space terms is described. Factorizations of inner functions are related bijectively to the set of invariant subspaces of a model operator, that is a restricted shift operator. By Finesso and Picci, factorization of inner functions to their state space realization can be related. The central result established a bijective correspondence between factorizations of an inner functions to their state space terms.