论文标题
polydegree $（n，1）$有理内部功能，切片矩阵和奇异性的注释
A note on polydegree $(n,1)$ rational inner functions, slice matrices, and singularities
论文作者
论文摘要
我们用polydegree $（n，1）$，$ n \ in \ mathbb {n}^{d-1} $分析了单元polydisk $ \ mathbb {d}^{d} $中理性内部函数的某些组成，以及$ \ \ m m mathbb {t}^d $。只要满足不可减至的条件，这种组成被证明是一个有理的内部函数，其位置与初始函数的位置完全相同，并且具有定量控制的特性。作为一个应用程序，我们回答了肯定中\ cite {bps22}中提出的问题的$ d $维版本。
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.
