We provide a comparative treatment of some aspects of spectral theory for
self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators
connected with the defocusing and focusing nonlinear Schr\"odinger equation, of
relevance to nonlinear optics.
In addition to a study of Dirac and Hamiltonian systems, we also introduce
the concept of Weyl-Titchmarsh half-line m-coefficients (and 2 x 2
matrix-valued M-matrices) in the non-self-adjoint context and derive some of
their basic properties. We conclude with an illustrative example showing that
crossing spectral arcs in the non-self-adjoint context imply the blowup of the
norm of spectral projections in the limit where the crossing point is
approached.
@article{0511369,
author = {Clark, Steve and Gesztesy, Fritz},
title = {On Self-adjoint and J-self-adjoint Dirac-type Operators: A Case Study},
journal = {arXiv},
volume = {2005},
number = {0},
year = {2005},
language = {en},
url = {http://dml.mathdoc.fr/item/0511369}
}
Clark, Steve; Gesztesy, Fritz. On Self-adjoint and J-self-adjoint Dirac-type Operators: A Case Study. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0511369/