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arXiv 2104.05461math.FA
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一类检验函数生成的巴拿赫代数的插值序列

Interpolating sequences for the Banach algebras generated by a class of test functions

Anindya Biswas, Vikramjeet Singh Chandel

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20 pages
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摘要：

给定$\mathbb{C}^n$中的域$Ω$和$Ω$上的检验函数$Ψ$的集合，我们考虑与对$(Ω,\,Ψ)$相关联的复值$Ψ$ -Schur-Agler类。本文刻画了以闭单位球为$Ψ$ -Schur-Agler类的相伴巴拿赫代数的插值序列.当$Ω$是复平面$\mathbb{C}$中的单位圆盘$\mathbb{D}$，且测试函数类只包含$\mathbb{D}$上的恒等函数时，上述代数是$\mathbb{D}$上的有界全纯函数代数，在这种情况下，我们的刻画退化为Carleson的著名结果.此外，我们提出了其他几种情况下的对$(Ω,\,Ψ)$，其中我们的主要结果可以应用于内插序列的特征，这也表明我们的主要结果的有效性。

英文摘要：

Given a domain $Ω$ in $\mathbb{C}^n$ and a collection of test functions $Ψ$ on $Ω$, we consider the complex-valued $Ψ$-Schur-Agler class associated to the pair $(Ω,\,Ψ)$. In this article, we characterize interpolating sequences for the associated Banach algebra of which the $Ψ$-Schur-Agler class is the closed unit ball. When $Ω$ is the unit disc $\mathbb{D}$ in the complex plane $\mathbb{C}$ and the class of test function includes only the identity function on $\mathbb{D}$, the aforementioned algebra is the algebra of bounded holomorphic functions on $\mathbb{D}$ and in this case, our characterization reduces to the well known result by Carleson. Furthermore, we present several other cases of the pair $(Ω,\,Ψ)$, where our main result could be applied to characterize interpolating sequences which also show the efficacy of our main result.

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