两个四阶微分算子积的自伴性  

Self-adjointness of Product of Two 4th-order Differential Operators

作　　者：杨传富[1] 黄振友[1] 杨孝平[1] 

机构地区：[1]南京理工大学理学院应用数学系,南京江苏210094

出　　处：《数学进展》2004年第3期291-302,共12页Advances in Mathematics（China）

摘　　要：本文研究由微分算式D^4-DpD+q生成的两个四阶微分算子L_i(i=1,2)的积L_2L_1的自伴性,并在常型和奇型情形下,分别获得了两个四阶微分算子积自伴的充要条件,同时证明了若L_1和L_2自伴,则L=L_2L_1自伴的充要条件是L_1=L_2。In this paper, we study the self-adjointness of product L_2L_1 of two 4th-order differential operators L_i(i=1, 2) generated by the diffrential expression D^4--DpD+q and obtain a necessary and sufficient condition for the self-adjoininess of product of two 4th-order differential operators, respectively, when both I=[a, b]and [0, ∞]. We prove that if both L_1 and L_2 are self-adjoint, then L=L_2L_1 is self-adjoint if and only if L_1=L_2.

关 键 词：自伴算子 两个微分算子积 边条件 

分 类 号：O175.3[理学—数学]