二阶幂零矩阵函数指数群的Wiener-Hopf分解  

Wiener-Hopf Factorization for a Group of Exponential of 2×2 Niopotent Matrix Functions

作　　者：郭国安[1] 肖兵[1] 方林[1] 

机构地区：[1]南京邮电大学理学院,江苏南京210023

出　　处：《南京邮电大学学报（自然科学版）》2014年第2期116-121,共6页Journal of Nanjing University of Posts and Telecommunications：Natural Science Edition

基　　金：国家自然科学基金(60972041);南京邮电大学引进人才科研启动基金(NY208070)资助项目

摘　　要：指数函数矩阵群在矩阵分解理论和应用中具有十分重要作用和意义,文中通过改进二阶幂零矩阵函数的结构,研究了一类二阶幂零矩阵函数指数群的Wiener-Hopf分解。给出了此类群满足典则Wiener-Hopf分解的充分必要条件;在此基础上又获得了相应的Riemann-Hilbert问题的一般解和Toeplitz算子的核空间的维数和非典则分解的偏执标结果;通过复杂地构造亚纯分解的显因式得到了典则分解的显因子式。A group of exponential matrix functions play an important role in the matrix factorization theo- ry. We focus on the research of Wiener-Hopf factorization of a group of expotential of 2 × 2 niopotent ma- trix function. A necessary and sufficient condition is given for a group of expotential of 2 × 2 niopotent matrix function which satisfy the canonical Wiener-Hopf factorization. The general solutions to the corre- sponding Riemann-Hilbert problem, dimentions of kernel space for Toeplitz operator and the partial indi- ces are obtained. Meanwhile, the canonical facotization explicitly by constructing its meromorphitc factori- zation explicitly is also obtained .

关 键 词：Wiener-Hopf分解 RIEMANN-HILBERT问题 亚纯分解 TOEPLITZ算子 

分 类 号：O175.5[理学—数学]