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

Radu Cascaval; Fritz Gesztesy

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

Radu Cascaval·Fritz Gesztesy

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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 Schrödinger hierarchy of evolution equations.

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BibTeX RIS

Radu Cascaval, Fritz Gesztesy. 2004-03-29. J-Self-Adjointness of a Class of Dirac-Type Operators. https://arxiv.org/abs/math/0403491

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