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中文摘要：
该文研究了无穷维Hamilton算子的特征函数系，给出了特征函数系在一般意义下不能完备的无穷维Hamilton算子的类．进而，解决了对一类无穷维Hamilton算子所对应的Hamilton系统能否可以应用传统分离变量法的问题．最后，举出了具体的例子，加以说明判别准则的有效性．
英文摘要：
In this paper, we study the eigenfunction systems of infinite dimensional Hamilto- nian operator and obtain a class of infinite dimensional Hamiltonian operators whose eigenfunc- tion systems are not complete in Hilbert space X × X, which is helpful to solve the problems that the method of separation of variable whether can be used in a class of Hamiltonian systems. In the end, concrete examples are constructed to justify the effectiveness of the criterion.
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