On the self-adjoint extensions of symmetric ordinary differential operators in direct sum spaces

Abstract

In this paper, we give the characterizations of self-adjoint domains for singular symmetric operators, by describing the boundary conditions of domain of conjugate differential operator, with interior singular points or in direct sum spaces. Last, we show that there exist other self-adjoint extension of T 0( M) which cannot be expressed as the direct sum of the self-adjoint extensions over the various subintervals.