论文标题
$ h^{\ infty}的某些亚级别上的nevanlinna-pick插值（\ mathbb {d}）$
Nevanlinna-Pick Interpolation On Certain Subalgebras of $H^{\infty}(\mathbb{D})$
论文作者
论文摘要
给定一个$ k $的正整数，令$ h^{\ infty} _k（\ m athbb {d}）$表示在单位磁盘$ \ mathbb {d} $中定义的所有有界分析函数的集合，in $ \ \ m mathbb {c} $ wht $ k^{ K $。 In this paper, we establish a Nevanlinna-Pick interpolation result for the subalgebra $H^{\infty}_K(\mathbb{D})$, where $K = \{1,2,\dotsc,k\}$, which is a slight generalization of the interpolation theorem that Davidson, Paulsen, Raghupathi, and Singh proved for the代数$ h^{\ infty} _ {\ {1 \}}（\ Mathbb {d}）$。此外，我们为给定的$ k $中的代数$ h^{\ mathbb {d}）$提供了足够的条件。最后，我们为存在这种插值功能提供了必要的条件。
Given a collection $K$ of positive integers, let $H^{\infty}_K(\mathbb{D})$ denote the set of all bounded analytic functions defined on the unit disk $\mathbb{D}$ in $\mathbb{C}$ whose $k^{\text{th}}$ derivative vanishes at zero, for all $k \in K$. In this paper, we establish a Nevanlinna-Pick interpolation result for the subalgebra $H^{\infty}_K(\mathbb{D})$, where $K = \{1,2,\dotsc,k\}$, which is a slight generalization of the interpolation theorem that Davidson, Paulsen, Raghupathi, and Singh proved for the algebra $H^{\infty}_{\{1\}}(\mathbb{D})$. Furthermore, we provide a sufficient condition for an interpolation function to exist in the algebra $H^{\infty}_K(\mathbb{D})$ for a given $K$. Lastly, we give a necessary condition for the existence of such interpolation functions.
