向量函数空间上两个极限圆型微分算子乘积的自伴性

On Self adjointness of the Product of Two Limit circle Differential Operators in Vector Function Spaces

讨论了在Ｌ２向量函数空间上由奇异形式自伴微分表达式定义的极限圆型乘积算子的最大算子域构造定理，并在此基础上得到了其自伴域的解析描述．乘积算子Ｔ＝Ｔ２Ｔ１自伴的充分必要条件是Ａ１Ｑ－１（０）Ａ＊２＝Ｂ１ＪＢ＊２，其中Ａｉ，Ｂｉ（ｉ＝１，２）决定了乘积算子的边界条件，即乘积算子自伴性由其边条件的性质唯一决定．

In the first,the structure of the maximum operator domains under the assumption that the limit circle product operator defined in L 2 vector function spaces are described.And then the analytical description of the corresponding self adjoint extention domains is obtained.The sufficient and necessary condition on self adjointness of the product operator T=T 2·T 1 is A 1Q -1 (0)A * 2=B 1JB * 2, where A i,B i(i=1,2) determine the boundary conditions of the product operator.That is,the self adjointness of the product operator is determined only by its boundary conditions.