奇型Sturm-Liouville微分算子的限界自伴扩张

Bound-Limited Self-Adjoint Extensions for Singular Sturm-Liouville Differential Operators

本文给出了奇型Sturm—Liouville微分算子限界自伴扩张的充要条件,从而得 到按边值条件分类的所有限界自伴边值条件,并直接回答了奇型Sturm—Liouville问题 的最小特征值不等式中相等的边值条件.

In this paper, a necessary and sufficient condition for an operator to be a bound-limited self-adjoint extension of a singluar Sturm-Liouville operator is obtained. As a consequence, all possible forms of the bound-limited self-adjoint extensions are characterized via complete classification of the self-adjoint boundary conditions. Also, this result can answer directly the equal cases of the inequalites among the minimal eigenvalues for singular Sturm-Liouville problems.