带位移退化Markushevich问题的求解  

SOME SOLUTIONS OF DEGENERATE MARKUSHEVICH PROBLEM WITH SHIFT

作　　者：曹长修[1] 陈金玉[1] 

机构地区：[1]重庆大学自动化学院控制工程系,重庆400044

出　　处：《应用数学学报》2001年第4期607-615,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家教育部博士生基金资助项目.

摘　　要：带位移Ｍａｒｋｕｓｈｅｖｉｃｈ问题 是１９４６年由Ｍａｒｋｕｓｈｅｖｉｃｈ Ａ Ｉ首先提出问题的推广，它们一并被得到广泛的研究，但是这 些研究大都只局限于其Ｎｏｅｔｈｅｒ性的讨论上，总是解的表达式，特别是封闭形式解，只局 限于单位圆上，月结论较为零星．本文讨论当Γ为简单封闭的Ｌｙａｐｕｎｏｖ曲线，且问题满 足退化条件｜Ｇ１（ｔ）｜＝｜Ｇ２（ｔ）｜≠０时，带位移 Ｍａｒｋｕｓｈｅｖｉｃｈ问题的求解．文章指出了其可解条 件及解的个数，给出了问题解的表达式，并在一些给定条件下，得出上述问题的封闭形式 解．本文包含了Ｇ．Ｓ．Ｌｉｔｖｉｎｃｈｕｋ的相关工作，并推广了王传荣的相应结果．In this paper the Markushevich problem with shift is investigated in the class of piecewise analytic functions. And it is generalized by Markushevich problem, which was first proposed in 1946. Many people advanced greatly the investigation of this problem, but the results were mostly in its Noether theorem. It is still difficult to find the expression of solution of the problem. When the degenerate condition is satisfied, we discuss the solvable condition of the Markushevich problem with shift and the number of its solution. Meanwhile, the author established the closed form of the solution of problem above, if some conditions are satisfied. Several well-known important conclusions on Markushevichs problem, such as Noether theorem in the degeneration, Wang chuan-rong result etc, can also be obtained as an immediate consequence of our results.

关 键 词：Markushevich问题 位移 Lyapunov曲线 同胚变换 分片解析函数 

分 类 号：O174.5[理学—数学]