论文标题
混凝土实现和麦卡锡香槟猜想的分析延续
Analytic continuation of concrete realizations and the McCarthy Champagne conjecture
论文作者
论文摘要
在本文中，我们提供了公式，使一个公式可以在传输函数类型的多变量schur，herglotz和挑选功能之间移动，而没有添加其他奇异性，除了可能来自共形变换本身的极点。在两变量的交换案例中，我们使用规范的de branges-rovnyak模型理论来获得具体实现，从而在分析上通过边界进行内部函数，这些函数在其中一个变量（所谓的准理性函数）中是合理的。然后，我们为麦卡锡的香槟猜想建立了积极的解决方案，以在两变量的准理性函数和$ d $ - 可变量的观点函数的设置中为本地矩阵单调性。
In this paper, we give formulas that allow one to move between transfer function type realizations of multi-variate Schur, Herglotz and Pick functions, without adding additional singularities except perhaps poles coming from the conformal transformation itself. In the two-variable commutative case, we use a canonical de Branges-Rovnyak model theory to obtain concrete realizations that analytically continue through the boundary for inner functions which are rational in one of the variables (so-called quasi-rational functions). We then establish a positive solution to McCarthy's Champagne conjecture for local to global matrix monotonicity in the settings of both two-variable quasi-rational functions and $d$-variable perspective functions.
