We provide a systematic study of boundary data maps, that is, 2 × 2 matrix-valuedDirichlet-to-Neumann and more generally, Robin-to-Robin maps, associated withone-dimensional Schrödinger operators on a compact interval [0, R] withseparated boundary conditions at 0 and R. Most of our results areformulated in the non-self-adjoint context.
Our principal results include explicit representations of these boundary data maps interms of the resolvent of the underlying Schrödinger operator and the associated boundarytrace maps, Krein-type resolvent formulas relating Schrödinger operators corresponding todifferent (separated) boundary conditions, and a derivation of the Herglotz property ofboundary data maps (up to right multiplication by an appropriate diagonal matrix) in thespecial self-adjoint case.
