JSelfAdjointness of a Class of DiracType Operators
Abstract
In this note we prove that the maximally defined operator associated with a class of Diractype differential expressions M(Q) is Jselfadjoint 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 Diractype differential expression M(Q) is of significance as it appears in the Lax formulation of the nonabelian (matrixvalued) focusing nonlinear Schrödinger hierarchy of evolution equations.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2004
 arXiv:
 arXiv:math/0403491
 Bibcode:
 2004math......3491C
 Keywords:

 Spectral Theory;
 Mathematical Physics;
 34L40;
 35Q55
 EPrint:
 8 pages. To appear in J. Math. Anal. Appl