2010/02/02 by Stephen Clark, Fritz Gesztesy, Clark, Stephen +3
Computer Science · Mathematics · Physics and Astronomy · #34B05 #34B20 #34B27 #34B40 #34L05 #34L40 #47A10 #47E05. #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:34B05 #msc:34B20 #msc:34B27 #msc:34B40 #msc:34L05 #msc:34L40 #msc:47A10 #msc:47E05.
paper · pdf · doi:10.48550/arxiv.1002.0606
40 pages
arxiv created 2010/02/02 · openalex publication_date 2010/02/02 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Schrodinger 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 Schrodinger operator and the associated boundary trace maps, Krein-type resolvent formulas relating Schrodinger 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.