一类六阶左定微分算子的谱

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

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≤…