常微分算子谱的定性分析

The Qualitative Analysis of the Spetrnm of Ordinary Differential Operators

本文时常微分算子谱的定性分析的若干问题做一综合性的概要介绍，着重介绍研究谱的定性分析的主要途径和研究方法；讨论谱的离散性判别准则及其发展和推广，列举一些在方法上有代表性的结论．文章分为五节：１谱的定性分析发展概况，研究的基本方法和途径；２二阶微分算子谱的离散性的判别；３高阶微分算子谱的离散性研究的发展现况；４加权的奇异微分算子谱的离散性的研究；５复系数Ｊ－自伴微分算子的离散谱。

This paper is a survey on some topics of the spectral qualitative analysis of or-dinary differential operators .We introduce the major methods of approach and the developmentof the research in this field, and put especial emphasis on the investigation of the nature of thespectrum,particularly, the decomposition criteria and the methods of expansion. We also listsome results on discrete spectrum, covering calses of the second-order,the high-order,weighted,and J-self adjoint differential operators.