Factorization and imbedding for general linear boundary value problems

A new direction in the theory of general linear boundary value problems is explored. The starting point is an explicit Volterra factorization of the Green's matrix (and related kernels) associated with the problem. This result leads to (1) imbedding of the boundary value problems, (2) initial value algorithms for their solution, and (3) comparison theorems relating two different boundary value problems with a common boundary condition. Extensions and connections with earlier work in this area are presented.