J-Self-Adjointness of a Class of Dirac-Type Operators
Spectral Theory
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
In this note we prove that the maximally defined operator associated with a class of Dirac-type differential expressions M(Q) is J-self-adjoint with respect to a proper antilinear conjugation J under the general hypothesis that the entries of the matrix potential coefficient Q are locally integrable on the real line. The Dirac-type differential expression M(Q) is of significance as it appears in the Lax formulation of the nonabelian (matrix-valued) focusing nonlinear Schr\"odinger hierarchy of evolution equations.
Cite
@article{arxiv.math/0403491,
title = {J-Self-Adjointness of a Class of Dirac-Type Operators},
author = {Radu Cascaval and Fritz Gesztesy},
journal= {arXiv preprint arXiv:math/0403491},
year = {2007}
}
Comments
8 pages. To appear in J. Math. Anal. Appl