一类高阶左定微分算子的谱  

Spectrum of a Class of High-order Left-definite Differential Operators

作　　者：高云兰[1] 孙炯[1] 

机构地区：[1]内蒙古大学理工学院数学系

出　　处：《内蒙古大学学报（自然科学版）》2005年第4期367-372,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(10261004);高等学校博士点专项科研基金(20040126008)

摘　　要：研究了一类高阶左定微分算子的谱,利用左定微分算子与右定微分算子的关系,得到结论:自伴边界条件的高阶左定微分算子的特征值均为实数,而且上无界下无界,且算子的特征值可以排序为…λ-2λ-1λ-0<0<λ0λ1λ2…The spectrum of a class of high-order left-definite differential operators was studied.Based on the relationship between the left-definite and the right-definite operators,a conclusion is obtained.If a high-order differential operator with a self-adjoint BC is left-definite and right-indefinite,then,all its eigenvalues are real.There exist countable,infinite,positive and negative eigenvalues,and they are unbounded from below and from above,have no finite cluster point,and can be indexed to satisfy the inequality: ...λ_(-2)λ_(-1)λ_(-0)<0<λ_0λ_1λ_2...

关 键 词：高阶微分算子 左定 特征值的存在 

分 类 号：O175.3[理学—数学]