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Boundary Data Maps for Schrödinger Operators on a Compact Interval
Published online by Cambridge University Press: 12 May 2010
Abstract
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.
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- Research Article
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- © EDP Sciences, 2010
Footnotes
Dedicated with deep admiration to the memory of Mikhail Sh. Birman (1928-2009)
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