四阶极限点型微分算子积的自伴边值问题

Self-adjoint Boundary Value for Products of Limit-point Fourth-order Differential Operators

在微分算式l(y)=y(4) -(py′)′+qy(t∈ [a,∞ ) )满足lk(y) (k=1,2)均为极限点型条件下,该文运用Calkin定理及微分算子自伴扩张理论,以边界条件形式研究了由l(y)生成的 2个微分算子积的自伴边值问题,并获得其自伴的充分必要条件,其结果对微分算子理论的研究是有益的。

For the differential expression l(y)=y (4)-(py′)′+qy,t∈Self-adjoint Boundary Value for Products of Limit-point Fourth-order Differential Operators $$$$ YANG Chuan-fu1,WANG Yu-ping2 (1.School of Sciences, NUST, Nanjing 210094, China; 2.College of Information Science and Technology, Nanjing Forest University, Nanjing 210037, China) Abstract: For the differential expression l(y)=y (4)-(py′)′+qy,t∈[a,∞), under the assumption that lk(y) (k=1,2) is limit-point, employing Calkin’s theorem and the theory of self-adjoint extensions of differential operators, we investigated the self-adjointness of product operator L 2L 1 where L i(i=1,2) are generated by l(y) with some boundary conditions. A necessary and sufficient condition for self-adjointness of L 2L 1 was obtained by boundary conditions. This result is useful in theory of the differential operators.