An expanded Phillips theory and its application to differential operators

A new characterization of maximal accretive extensions of accretive operators is presented. It is based on expanded spaces of the abstract boundary spaces developed by R.S. Phillips, and is therefore called the expanded Phillips theory. In particular, when the operator is symmetric, a concrete realization of the expanded spaces is given. In applications of the expanded Phillips theory to ordinary differential equations, we characterize all maximal accretive extensions of singular symmetric ordinary differential operators of order 2n.