Dirac type and canonical systems: spectral and Weyl–Titchmarsh matrixfunctions, direct and inverse problems

Abstract

The direct spectral problem for the matrix Dirac type systems with locallysummable potentials and the inverse spectral problem for the matrixDirac type systems with locally bounded potentials are solved on theinterval and on the half-line. A direct procedure to recover the potential bythe Weyl–Titchmarsh function is given also. Some important corollarieson the high-energy asymptotics of the Weyl–Titchmarsh functions andon the local uniqueness for the corresponding inverse problem follow.New results are obtained for the general type canonical systems also.