论文标题
在完整的选择空间中免费的外部功能
Free outer functions in complete Pick spaces
论文作者
论文摘要
陪审团和马丁建立了耐力空间功能的经典内在分解的类似物。他们表明，带有归一化完整挑选内核的希尔伯特功能空间中的每个功能$ f $都具有$ f =φg$的类型分解，其中$ g $是循环的，$φ$是承包的乘数，$ \ | f \ | f \ | = \ | = \ | g \ \ \ \ | $。在本文中，我们表明，如果假定循环因子是我们所说的自由外部，那么这些因素本质上是独一无二的，我们给出了空间内部因素的特征。这使我们可以计算示例。我们还提供了这种分解的几种应用。
Jury and Martin establish an analogue of the classical inner-outer factorization of Hardy space functions. They show that every function $f$ in a Hilbert function space with a normalized complete Pick reproducing kernel has a factorization of the type $f=φg$, where $g$ is cyclic, $φ$ is a contractive multiplier, and $\|f\|=\|g\|$. In this paper we show that if the cyclic factor is assumed to be what we call free outer, then the factors are essentially unique, and we give a characterization of the factors that is intrinsic to the space. That lets us compute examples. We also provide several applications of this factorization.
