论文标题
Bidisc上的Schur功能和内部功能
Schur functions and inner functions on the bidisc
论文作者
论文摘要
我们从分数线性变换的角度研究了Bidisc上内部功能的表示，并在凸起矩阵方面提供了足够的条件，以实现两种可变性的内部功能。在这里，通常不需要足够的条件，我们证明了接纳一个可变分解的理性内部函数的弱相反。 我们提出了BIDISC上De Branges-Rovnyak内核的完整分类（在Polydisc的设置和$ \ Mathbb {C}^n $，$ n \ geq 1 $的开放单元球和开放单位球上同样起作用。我们还根据Agler内核进行分类，两变量的Schur函数吸收了一个可变因素。
We study representations of inner functions on the bidisc from a fractional linear transformation point of view, and provide sufficient conditions, in terms of colligation matrices, for the existence of two-variable inner functions. Here the sufficient conditions are not necessary in general, and we prove a weak converse for rational inner functions that admit one variable factorization. We present a complete classification of de Branges-Rovnyak kernels on the bidisc (which equally works in the setting of polydisc and the open unit ball of $\mathbb{C}^n$, $n \geq 1$). We also classify, in terms of Agler kernels, two-variable Schur functions that admit one variable factor.
