论文标题
与外部功能插值
Interpolating with outer functions
论文作者
论文摘要
Mittag-Leffler和Weierstrass的经典定理表明，当$ \ {λ_n\} $是开放单位磁盘$ \ d $中的一系列不同点时，在$ \ d $中没有积聚点，$ \ d $，$ \ \ \ \ {w_n \} $是$ $ $ n $ n $ n $ d的$ n $ n n $ ns $ n dem / w_n $。 Carleson \ cite {MR117349}的著名定理是指何时，对于有限的序列$ \ {w_n \} $，可以通过有界的分析功能来解决这个插值问题。 Earl \ cite {MR284588}的定理进一步表明，当满足Carleson的条件时，插值函数$ ϕ $可能是Blaschke产品的常数倍数。在本文中，我们探讨何时插值$ ϕ $可以是外部功能。然后，我们使用我们的结果来完善McCarthy \ cite {MR1065054}的结果，并在模型空间上探索共分析toeplitz运算符的共同范围。
The classical theorems of Mittag-Leffler and Weierstrass show that when $\{λ_n\}$ is a sequence of distinct points in the open unit disk $\D$, with no accumulation points in $\D$, and $\{w_n\}$ is any sequence of complex numbers, there is an analytic function $ϕ$ on $\D$ for which $ϕ(λ_n) = w_n$. A celebrated theorem of Carleson \cite{MR117349} characterizes when, for a bounded sequence $\{w_n\}$, this interpolating problem can be solved with a bounded analytic function. A theorem of Earl \cite{MR284588} goes further and shows that when Carleson's condition is satisfied, the interpolating function $ϕ$ can be a constant multiple of a Blaschke product. In this paper, we explore when the interpolating $ϕ$ can be an outer function. We then use our results to refine a result of McCarthy \cite{MR1065054} and explore the common range of the co-analytic Toeplitz operators on a model space.
