对称多圆盘的函数论性质及其推广
Function theoretic aspects of the symmetrized polydisc and generalization
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中文总结 AI 辅助
本文研究对称多圆盘$\boldsymbol{\reals^d}$的函数论性质，引入Schur-Agler型类并建立相关定理，还将这些结果推广至更一般的对称域族$\boldsymbol{\theta_d}$。
中文摘要 AI 辅助
我们针对对称多圆盘$\boldsymbol{\reals^d}$引入Schur-Agler型类，并建立该类函数的实现定理；陈述并证明$\boldsymbol{\reals^d}$上的插值定理，其中插值函数属于对应的Schur-Agler型类；还为$\boldsymbol{\reals^d}$建立Toeplitz corona定理与扩张定理，并将上述实现、插值、Toeplitz corona及扩张定理推广至更一般的对称域族$\boldsymbol{\theta_d}$。
英文摘要
We introduce Schur-Agler type class for the symmetrized polydisc $\mathbb{G}_d$ and establish a realization theorem for functions in this class. We state and prove an interpolation theorem on $\mathbb{G}_d$ with interpolating functions belonging to the associated Schur-Agler type class. Moreover, Toeplitz corona and extension theorems are established for $\mathbb{G}_d$. We also extend the realization, interpolation, Toeplitz corona and extension theorems to a more general symmetrized family of domains $Θ_d$.
