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

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

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