Duality Theory for nth Order Differential Operators under Stieltjes Boundary Conditions

The adjoint of an nth order vector-valued linear differential system with boundary conditions represented by singular matrix-valued measures is constructed when the system is viewed as an operator with domain and range in a space of $L^p $ integrable functions. Both the operator and its adjoint are shown to be normally solvable. The theory is then applied to the multipoint boundary value problem of Wilder, and some examples are discussed.