We provide a systematic study of boundary data maps, that is, 2 × 2 matrix-valued
Dirichlet-to-Neumann and more generally, Robin-to-Robin maps, associated with
one-dimensional Schrödinger operators on a compact interval [0, R] with
separated boundary conditions at 0 and R. Most of our results are
formulated in the non-self-adjoint context.
Our principal results include explicit representations of these boundary data maps in
terms of the resolvent of the underlying Schrödinger operator and the associated boundary
trace maps, Krein-type resolvent formulas relating Schrödinger operators corresponding to
different (separated) boundary conditions, and a derivation of the Herglotz property of
boundary data maps (up to right multiplication by an appropriate diagonal matrix) in the
special self-adjoint case.