极限点型 Sturm-Liouville 算子乘积的自伴性

假设微分算式l(y)=-(py') qy,t∈a,∞),满足lk(y)(k=1,2,3)均为极限点型,作者研究了由l(y)生成的两个微分算子Li(i=1,2)的乘积L2L1的自伴性问题并获得其自伴的充分必要条件．同时研究了由l(y)=-y" qy,t∈a,∞),生成的三个微分算子Li(i=1,2,3)的乘积L3L2L1的自伴性问题．

Self-Adjointness Of Products Of The Limit-Point Sturm-Liouville Operators

For the differential expression $l(y)=-(py')'+qy, \ t\in a,\infty)$, under the assumption that $l^k\ (k=1,2,3)$ are limit-pointed, the author studies the self-adjointness of the product operator $L_2L_1$, which $L_i\ (i=1,2)$ are generated by $l(y)$, and obtains a necessary and sufficient condition for self-adjointness of $L_2L_1$. Also, a necessary and sufficient condition for the self-adjointness of $L_3L_2L_1$, which $L_i\ (i=1,2,3)$ are associated with $l(y)=-y'+qy, \ t\in a,\infty)$, is obtained.