Abstract. We consider the non-self-adjoint matrix equation of Dirac type on the line. For this case we introduce and investigate the Weyl–Titchmarsh matrix functions. We then obtain the Weyl–Titchmarsh matrix functions of Dirac-type equations with a shifted argument. Furthermore, we construct a class of the Weyl–Titchmarsh matrix functions generating potentials of the finite-band type. Using the above-mentioned results we deduce the matrix analogue of the trace formula. We consider separately the scalar case of Dirac-type equations.

Print publication: Issue 6 (December 2002)
Received 14 February 2002, in final form 26 September 2002
Published 18 October 2002