Friedrichs, Extension Theory Of Ordinary Differential Operators

The Friedrichs extension of semibounded operators is widely used in mathematical physics. The Priedrichs extension and more general energetic extension of symmetric operators are the functional analytic core of mathematical physics. So , first .we synthesize the materials on the method of the Priedrichs extension , its characteristics and its background of mathematical physics. Next we show that the relation between the Priedrichs extension , the Calkin extension and the von Neumann extension on the 2n-th order real symmetric ordinary differential operators , i.e. the relation of the boundary value corresponding to Priedrichs extension , the matrix to the Calkin extension and the unitary operator to the von Neumann extension.