FREE OUTER FUNCTIONS IN COMPLETE PICK SPACES

Jury and Martin establish an analogue of the classical inner-outer factorization of Hardy space functions. They show that every function f in a Hilbert function space with a normalized complete Pick reproducing kernel has a factorization of the type f = phi g, where g is cyclic, phi is a contractive multiplier, and parallel to f parallel to = parallel to g parallel to. In this paper we show that if the cyclic factor is assumed to be what we call free outer, then the factors are essentially unique, and we give a characterization of the factors that is intrinsic to the space. That lets us compute examples. We also provide several applications of this factorization.

Automated summary

This paper investigates the inner-outer factorization of Hardy space functions and shows that under certain conditions, the factors of this factorization are essentially unique. Several applications of this factorization are also provided.