J-Self-Adjointness of a Class of Dirac-Type Operators

Details J-Self-Adjointness of a Class of Dirac-Type Operators J-Self-Adjointness of a Class of Dirac-Type Operators

2004-03-29

arxiv.org/abs/math/0403491v1

Mathematics

Spectral Theory

8 pages. To appear in J. Math. Anal. Appl

Scientific paper

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.

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