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arXiv · 2206.02752

Subinner-free outer factorizations on an annulus

Georgios Tsikalas
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Abstract

Recent work of Aleman, Hartz, McCarthy and Richter generalizes the classical inner-outer factorization of Hardy space functions to the complete Pick space setting, establishing an essentially unique "subinner-free outer" factorization. In this note, we investigate certain special examples of such factorizations in the setting of the function space induced on the annulus $A_r=\{r<|z|<1\}$ by the complete Pick kernel $$k_{r}(λ,μ):=\frac{1-r^2}{(1-λ\barμ)(1-r^2/λ\barμ)}.$$

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Georgios Tsikalas. 2022-06-06. Subinner-free outer factorizations on an annulus. https://arxiv.org/abs/2206.02752

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