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Inverse problem to recover the skew-self-adjoint Dirac-type system from thegeneralized Weyl matrix function is treated in the paper. Sufficient conditionsunder which the unique solution of the inverse problem exists, are formulatedin terms of the Weyl function and a procedure to solve the inverse problem isgiven. The case of the generalized Weyl functions of the form$\phi(\lambda)\exp\{-2i\lambda D\}$, where $\phi$ is a strictly proper rationalmatrix function and $D=D^* \geq 0$ is a diagonal matrix, is treated in greaterdetail. Explicit formulas for the inversion of the corresponding semiseparableintegral operators and recovery of the Dirac-type system are obtained for thiscase.

Semiseparable integral operators and explicit solution of an inverse problem for the skew-self-adjoint Dirac-type system