一类常微分算子的谱分析  

Spectral Analysis of a Class of Ordinary Differential Operators

作　　者：刘超[1] 孙炯[1] 

机构地区：[1]内蒙古大学数学系,呼和浩特010021

出　　处：《内蒙古大学学报（自然科学版）》2004年第5期495-500,共6页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金资助项目(19871037);内蒙古大学青年科学基金资助项目(ND0203)

摘　　要：研究了一类具有对数函数系数的常微分算子,使用酉变换和不等式估计给出了本质谱分布的范围和本质谱为空集时系数应满足的条件,通过与常系数微分算子及Euler微分算子的比较,分析了系数的变化对本质谱的影响.A class of differential operators with logarithmic coefficients is investigated. Using the methods of unitary transformation and inequality estimation, we obtain the distribution of the essential spectrum, and give some conditions satisfied by coefficients of differential operators, which guarantee that the essential spectrum is empty.The influence of coefficients on the essential spectrum is also studied by comparing them with the constant coefficient differential operators and the Euler differential operators.

关 键 词：微分算子 本质谱 D-算子 

分 类 号：O175.3[理学—数学]