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arXiv · 2203.08179

Free outer functions in complete Pick spaces

Alexandru Aleman·Michael Hartz·John E. McCarthy·Stefan Richter
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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 $f=\varphi g$, where $g$ is cyclic, $\varphi$ 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.

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Alexandru Aleman, Michael Hartz, John E. McCarthy, Stefan Richter. 2022-03-15. Free outer functions in complete Pick spaces. https://arxiv.org/abs/2203.08179

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