We provide a systematic study of boundary data maps, that is, 2 x 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.


Mathematics and Statistics


Based upon work partially supported by the US National Science Foundation under Grant Nos. DMS-0400639 and FRG-0456306.

Keywords and Phrases

Boundary data; Krein-type resolvent formulas; Linear Fractional Transformations; Robin-to-Robin maps; Separated boundary conditions; Linear transformations; Boundary conditions; (Non-self-adjoint) Schrödinger operators on a compact interval; Boundary data maps; Krein-type resolvent formulas; Linear fractional transformations; Separated boundary conditions

International Standard Serial Number (ISSN)

0973-5348; 1760-6101

Document Type

Article - Journal

Document Version

Final Version

File Type





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Publication Date

01 Jan 2010