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arXiv · 2207.08961

A note on polydegree $(n,1)$ rational inner functions, slice matrices, and singularities

Alan Sola
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Abstract

We analyze certain compositions of rational inner functions in the unit polydisk $\mathbb{D}^{d}$ with polydegree $(n,1)$, $n\in \mathbb{N}^{d-1}$, and isolated singularities in $\mathbb{T}^d$. Provided an irreducibility condition is met, such a composition is shown to be a rational inner function with singularities in precisely the same location as those of the initial function, and with quantitatively controlled properties. As an application, we answer a $d$-dimensional version of a question posed in \cite{BPS22} in the affirmative.

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Alan Sola. 2022-07-18. A note on polydegree $(n,1)$ rational inner functions, slice matrices, and singularities. https://arxiv.org/abs/2207.08961

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