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arXiv · 1708.05593

Factorizations induced by complete Nevanlinna-Pick factors

Alexandru Aleman·Michael Hartz·John E. McCarthy·Stefan Richter
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Abstract

We prove a factorization theorem for reproducing kernel Hilbert spaces whose kernel has a normalized complete Nevanlinna-Pick factor. This result relates the functions in the original space to pointwise multipliers determined by the Nevanlinna-Pick kernel and has a number of interesting applications. For example, for a large class of spaces including Dirichlet and Drury-Arveson spaces, we construct for every function $f$ in the space a pluriharmonic majorant of $|f|^2$ with the property that whenever the majorant is bounded, the corresponding function $f$ is a pointwise multiplier.

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Alexandru Aleman, Michael Hartz, John E. McCarthy, Stefan Richter. 2017-08-18. Factorizations induced by complete Nevanlinna-Pick factors. https://doi.org/10.1016/j.aim.2018.07.013

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