J-self-adjointness of a class of Dirac-type operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:294

Article

Cascaval, R ; Gesztesy, F

关键词: Dirac-type operator;    J-self-adjointness;   

DOI  :  10.1016/j.jmaa.2004.02.002

来源: Elsevier

【 摘 要 】

In this note, we prove that the maximally defined operator associated with the Dirac-type differential expression M (Q) = i (d/dxI(m) -Q -Q* -d/dxI(m)) where Q represents a symmetric m x m matrix (i.e., Q(x)inverted perpendicular = Q(x) a.e.) with entries in L-loc(1)(R), is J-self-adjoint, where J is the antilinear conjugation defined by J = sigma(1)C, sigma = (0 I-m I-m 0) and C(a(1),..., a(m), b(1),..., b(m))inverted perpendicular = ((a) over bar (1),.., (a) over bar (m), (b) over bar (1),..., (b) over bar (m))inverted perpendicular. The differential expression M(Q) is of significance as it appears in the Lax formulation of the non-abelian (matrix-valued) focusing nonlinear Schrodinger hierarchy of evolution equations. (C) 2004 Elsevier Inc. All rights reserved.

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