On The Self-Adjointness Of Product Of Two Odd-Order Differential Operators

In this paper, the adjointness of the product of two differential operators generated by a third order normal and singular symmetric differential expression in the limit-circle case is discussed. The necessary and sufficient conditions which make the product operators being the adjoint operators obtained by the matrix analysis and calculation. At the same time, the adjointness of the product of the power and adjointness operator obtained. Here we note that the coefficients of the third order symmetric differential expression are complex, the coefficients of the product of operator is real. There is a lot of difference between of the even order and odd order.On this basis,the asjointness of the product of two high order operators generated by a high order normal and singular symmetric differential expression in the limit-circle case is discussed, and comparing of the third-order situation, a number of other similar conclusions obtained.