标题： 单位圆上的规范Wiener-Hopf分解：匹配子空间与Riccati方程 显示英文标题

标题： Canonical Wiener-Hopf factorization on the unit circle: matching subspaces versus Riccati equations

摘要： 维纳-霍普夫分解是研究块托普利茨和块维纳-霍普夫算子的重要工具，涉及这些算子的许多应用。 在本文中，我们比较了两种维纳-霍普夫分解的方法，即基于匹配不变子空间的更经典的方法和基于非对称里卡蒂方程解的较新方法。 后一种方法扩展到了希尔伯特空间算子值函数的情况，这些函数在单位圆盘的邻域内是解析的$\BT$，但不必是有理的。 在两种方法中，规范右维纳-霍普夫分解的存在性由里卡蒂方程的稳定解的存在性来表征，然而，里卡蒂方程并不相同。 我们分析了里卡蒂方程的解集，并证明它们确实不同，但它们具有相同的稳定解。 显示英文摘要

摘要： Wiener-Hopf factorization is an important tool in the study of block Toeplitz and block Wiener-Hopf operators, and many applications involving these operators. In this paper we compare two approaches to Wiener-Hopf factorization, namely, the more classical approach based on matching invariant subspaces and a more recent approach based on solutions to a non-symmetric Riccati equation. The latter approach is extended to the case of Hilbert space operator-valued functions that are analytic on a neighborhood of the unit disc $\BT$, but need not be rational. In both approaches, existence of canonical right Wiener-Hopf factorization is characterized by existence of a stabilizing solution to a Riccati equation, however, the Riccati equations are not the same. We analyse the solution sets of the Riccati equations and show that they indeed are not the same, but they do have the same stabilizing solution.