全纯矩阵函数的解析性质

发布时间：2018-06-06 21:50

本文选题：Picard型定理 + 全纯矩阵函数　；参考：《北京邮电大学》2017年硕士论文

【摘要】：值分布和复动力系统是复分析中两个重要的研究方向。本文把亚纯函数的动力学性质和值分布理论推广到了一类全纯矩阵函数上。首先,利用复分析和矩阵分析的相关知识,我们研究了与整函数f相对应的C2×2矩阵空间上的全纯矩阵函数F的解析性质,给出了C2×2矩阵空间上全纯矩阵函数的Picard型定理,同时得到了全纯矩阵函数存在例外值的充分必要条件。利用整函数渐近值性质,建立了全纯矩阵函数例外值与渐近值之间的联系。我们还研究了全纯矩阵函数周期点的性质,得到了相对应的整函数f的Julia集的特征。进一步,将C2×2矩阵空间的全纯矩阵函数的相关性质推广到了一般高维矩阵函数上,得到了与整函数f相对应的Cn×n矩阵空间上的全纯矩阵函数F的解析性质。
[Abstract]:The value distribution and the complex dynamic system are two important research directions in complex analysis. In this paper, the dynamic properties of meromorphic functions and the theory of value distribution are generalized to a class of holomorphic matrix functions. First, by using the related knowledge of complex analysis and matrix analysis, we have studied the Holomorphic matrix functions of the C2 x 2 matrix space corresponding to the whole function f. The Picard type theorem of the Holomorphic matrix function in the space of C2 x 2 matrix is given, and the necessary and sufficient conditions for the existence of the exceptional value of the Holomorphic matrix function are obtained. The connection between the exceptional value of the Holomorphic matrix function and the asymptotic value is established by using the asymptotic property of the whole function. We also study the periodic point of the Holomorphic matrix function. The properties of the Julia set of the corresponding integral function f are obtained. Further, the related properties of the Holomorphic matrix function of the C2 x 2 matrix space are generalized to the general high dimensional matrix function, and the solution properties of the Holomorphic matrix function F on the Cn * n matrix space corresponding to the whole function F are obtained.
【学位授予单位】：北京邮电大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O151.21;O174.52

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