微分算子的自共轭域和谱分析——微分算子研究在内蒙古大学三十年  

Characterization of Domains of Self-Adjoint Ordinary Differential Operators and Spectral Analysis

作　　者：孙炯[1] 王万义[1] 

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《内蒙古大学学报（自然科学版）》2009年第4期469-485,共17页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10861008);(10661008);内蒙古自然科学基金重点项目(200711020102)

摘　　要：对常微分算子的自共轭域和谱分析的若干问题作了综合性的概要介绍.着重介绍了微分算子的自共轭扩张、自共轭域的辛几何刻画、空间中实参数解的个数对于连续谱的影响、谱的离散性、带有不定权函数的微分算子、不连续点的Sturm-Liouville问题的谱分析以及微分算子特征值的数值方法等问题的研究进展和研究方法,特别是内蒙古大学微分算子讨论班在近30年来在这些领域所做的工作.This is a survey on some topics of the characterization of domains of self-adjoint ordinary differential operators and spectral analysis. The major methods and development of the research in this field are introduced including domains of self-adjoint ordinary differential operators, symplectic structure of self-adjoint domains,the connection between square-integrable solutions for real values of the spectral parameter and the continuous spectrum of self-adjoint ordinary differential operators, the discreetnessof spectrum, the spectral analysis of non-definite differential operators, discontinuous Sturm-Liouville problems and numerical computation of eigenvalues of differential operators, especially the development of research at Inner Mongolia University in the last 30 years.

关 键 词：微分算子 亏指数 自共轭域 谱分析 数值计算 

分 类 号：O175.3[理学—数学]