Free outer functions in complete Pick spaces [article]

Alexandru Aleman, Michael Hartz, John E. McCarthy, Stefan Richter
2022 arXiv   pre-print
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=φ g, where g is cyclic, φ is a contractive multiplier, and f=g. 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
more » ... intrinsic to the space. That lets us compute examples. We also provide several applications of this factorization.
arXiv:2203.08179v1 fatcat:s7i7jfyiancoznzgz7fjyoakyi