# Boundary Data Maps for Schrödinger Operators on a Compact Interval

S. Clark; F. Gesztesy; M. Mitrea

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 5, Issue: 4, page 73-121
- ISSN: 0973-5348

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topClark, S., Gesztesy, F., and Mitrea, M.. "Boundary Data Maps for Schrödinger Operators on a Compact Interval." Mathematical Modelling of Natural Phenomena 5.4 (2010): 73-121. <http://eudml.org/doc/197614>.

@article{Clark2010,

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.},

author = {Clark, S., Gesztesy, F., Mitrea, M.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {(non-self-adjoint) Schrödinger operators on a compact interval; separated boundary conditions; boundary data maps; Robin-to-Robin maps; linear fractional transformations; Krein-type resolvent formulas; Kreĭn-type resolvent formulas},

language = {eng},

month = {5},

number = {4},

pages = {73-121},

publisher = {EDP Sciences},

title = {Boundary Data Maps for Schrödinger Operators on a Compact Interval},

url = {http://eudml.org/doc/197614},

volume = {5},

year = {2010},

}

TY - JOUR

AU - Clark, S.

AU - Gesztesy, F.

AU - Mitrea, M.

TI - Boundary Data Maps for Schrödinger Operators on a Compact Interval

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/5//

PB - EDP Sciences

VL - 5

IS - 4

SP - 73

EP - 121

AB - 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.

LA - eng

KW - (non-self-adjoint) Schrödinger operators on a compact interval; separated boundary conditions; boundary data maps; Robin-to-Robin maps; linear fractional transformations; Krein-type resolvent formulas; Kreĭn-type resolvent formulas

UR - http://eudml.org/doc/197614

ER -

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