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中文摘要：
该文研究一类时滞方程解的展开问题．研究的模型来自于实际高精密切割过程中具有时间延迟的机床振动问题．对此模型，借助于泛函分析方法，将其写成抽象发展方程．对系统确定的算子给出了较细致的谱分析，得到本征值的渐近表达式．同时证明相应的本征向量不能构成状态空间基，但给出方程解的展开式．
英文摘要：
In this paper, the authors investigate the spectrum and expansion of solutions for a class of delay differential equations. The model under consideration comes from a practical problem, which describes machine tool vibration in cutting process. They tranform the model into a first order differential equation in a Hilbert state space. And then using the theory of Co semigroup, they obtain the well-posed-hess of the sytem. By a detailed spectrum analysis, they give an explicit asymptotic expression of all eigenvalues. In addtion, they show that the eigenfunctions of the system do not form a basis for the state space; however, they get the exspansion of solution of the system according to the eigenfunctions.
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