The Symplectic Geometry Description Of The Self-Adjoint Domains Of Differential Operators On Infinite Interval

The discription of the self-adjoint domains of differential operators is one of the basic questions.The results of ordinary differential operators have been obtained in 50s'.Scientists' attention is paid to the discription of the self-adjoint boundary condi-tions of singular differential operators during 50 years recently. In this paper,we build symplectic structure of 2-nd order and high order singular differential operators on infinite interval, we construct a symplectic space by the maximal and minimal operator domain . Using Lagrangian submanifold in symplectic space ,we give a complete discription and classification of the self-adjoint domains of the 2-nd order and high order singular differential operators on infinite interval .