Formally self-adjoint quasi-differential operators and boundary-value problems

Abstract

We develop the machinery of boundary triplets for one-dimensional operators generated by formally self-adjoint quasi-differential expression of arbitrary order on a finite interval. The technique is then used to describe all maximal dissipative, accumulative and self-adjoint extensions of the associated minimal operator and its generalized resolvents in terms of the boundary conditions. Some specific classes are considered in greater detail.

Keywords

• Quasi-differential operator
• distributional coefficients
• self-adjoint extension
• maximal dissipative extension
• generalized resolvent