The Self-Adjointness Of Product Of Four Second-Order Differential Operators

In this paper, the adjointness of the product of four differential operators generated by a second order normal symmetric differential expression is discussed. We translate the problem of the product of four differential operator into the problem of the product of two differential operators. The necessary and sufficient conditions which make the product operators being the adjoint operators obtained by the adjoint operators analysis and matrix analysis and calculation. At the same time, the adjointness of the product of the power and adjointness operator obtained. On this basis, the adjointness of the product of four second order operators generated by a second order singular symmetric differential expression is discussed, a number of other similar conclusions obtained.