## Abstract

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 = ϕg, 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 is intrinsic to the space. That lets us compute examples. We also provide several applications of this factorization.

Original language | English |
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Pages (from-to) | 1929-1978 |

Number of pages | 50 |

Journal | Transactions of the American Mathematical Society |

Volume | 376 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1 2023 |