Self-adjoint problems for nondensely defined ordinary differential operators and their eigenfunction expansions

Abstract

The self-adjoint subspace extensions of a possibly nondensely defined symmetric ordinary differential operator in a Hilbert space are described. The operator part of these extensions involve not only the differential operator but boundary-integral terms, and the side conditions which determine the domains of the extensions also involve boundary-integral terms. Corresponding to each self-adjoint subspace extension in a possibly larger Hilbert space an eigenfunction expansion result is obtained. Analogous results for first-order systems of ordinary differential operators are shown to be valid.