| 二阶幂零矩阵函数指数群的Wiener-Hopf分解 |
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| 引用本文： | 郭国安,肖兵,方林.二阶幂零矩阵函数指数群的Wiener-Hopf分解[J].南京邮电大学学报(自然科学版),2014(2):116-121. |
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| 作者姓名： | 郭国安 肖兵 方林 |
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| 作者单位： | 南京邮电大学理学院,江苏南京210023 |
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| 基金项目： | 国家自然科学基金（60972041）和南京邮电大学引进人才科研启动基金（NY208070）资助项目 |
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| 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.
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| 关 键 词： | Wiener-Hopf分解 Riemann-Hilbert问题 亚纯分解 Toeplitz算子 |
Wiener-Hopf Factorization for a Group of Exponential of 2×2 Niopotent Matrix Functions |
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| GUO Guo-an,XIAO Bing,FANG Lin.Wiener-Hopf Factorization for a Group of Exponential of 2×2 Niopotent Matrix Functions[J].Journal of Nanjing University of Posts and Telecommunications,2014(2):116-121. |
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| Authors: | GUO Guo-an XIAO Bing FANG Lin |
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| Institution: | ( College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China) |
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| Abstract: | 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 . |
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| Keywords: | Wiener-Hopf factorization Riemann-Hilbert problem meromorphic factorization Toeplitz op- erator |
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