论文标题
凸起可逆锥和nevanlinna-pick插值：次优案
Convex invertible cones and Nevanlinna-Pick interpolation: The suboptimal case
论文作者
论文摘要
Nevanlinna-Pick插值从经典复杂分析的主题开发到解决控制理论和电气工程中各种问题的有用工具。多年来，考虑了原始问题的许多扩展，包括扩展到不同功能空间，非平稳问题，几个可变设置以及与矩阵和操作员点的插值。在这里，我们讨论了Nevanlinna-pick插值的变化，用于在实际基质点中评估的正真实奇数函数。 Cohen和Lewkowicz使用凸逆锥和Lyapunov Order研究了这个问题，但从未完全解决。在本文中，我们在一种特殊情况下提出了解决此问题的解决方案，我们根据与经典案例的联系称为“次优”。该解决方案需要表示可以追溯到R.D. Hill的线性矩阵映射，并分析何时正线性矩阵映射完全正面，我们在早期工作中进行了报告，并在此处简要审查。
Nevanlinna-Pick interpolation developed from a topic in classical complex analysis to a useful tool for solving various problems in control theory and electrical engineering. Over the years many extensions of the original problem were considered, including extensions to different function spaces, nonstationary problems, several variable settings and interpolation with matrix and operator points. Here we discuss a variation on Nevanlinna-Pick interpolation for positive real odd functions evaluated in real matrix points. This problem was studied by Cohen and Lewkowicz using convex invertible cones and the Lyapunov order, but was never fully resolved. In this paper we present a solution to this problem in a special case that we refer to as `suboptimal' based on connections with the classical case. The solution requires a representation of linear matrix maps going back to R.D. Hill and an analysis of when positive linear matrix maps are completely positive, on which we reported in earlier work and which we will briefly review here.
