一类六阶左定微分算子的谱  

THE SPECTRUM OF A CLASS OF SIX-ORDER LEFT-DEFINITE DIFFERENTIAL OPERATORS

作　　者：高云兰[1] 孙炯[2] 

机构地区：[1]内蒙古工业大学理学院,呼和浩特010051 [2]内蒙古大学理工学院,呼和浩特010021

出　　处：《内蒙古工业大学学报（自然科学版）》2008年第1期1-5,共5页Journal of Inner Mongolia University of Technology：Natural Science Edition

基　　金：国家自然科学基金资助项目(10561005);教育部博士学科点专项科研基金(20040126008)

摘　　要：本文研究了一类六阶左定微分算子的谱,利用krein空间中不定微分算子的特征以及左定微分算子与右定微分算子的关系,得到结论:自伴边界条件的六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-2≤λ-1≤λ-0<0<λ0≤λ1≤λ2≤…In this paper,a study on the spectrum of a class of six-order left-definite differential operators is presented. Characteristics of the non-definite differential operators in Krein space and the relationship between the left-definite and the right-definite operators are used for the study. A conclusion is drawn that,if a six-order differential operator with a self-adjoint BC is left-definite and right-indefinite, then all its eigenvalues are real, moreover, there exist many infinitely countable positive and negative eigenvalues,and they are unbounded upward and downward. They have no finite cluster point and can be indexed to satisfy the inequalities： …≤λ-2≤λ-1≤λ-0〈0〈λ0≤λ-1≤λ-2≤…

关 键 词：左定微分算子 不定微分算子 KREIN空间 特征值的存在 

分 类 号：O175.3[理学—数学]