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

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

2009-04-15

arxiv.org/abs/0904.2357v1

Integral Equations and Operator Theory (2010)

Mathematics

Classical Analysis and ODEs

Scientific paper

10.1007/s00020-010-1739-1

Inverse problem to recover the skew-self-adjoint Dirac-type system from the generalized Weyl matrix function is treated in the paper. Sufficient conditions under which the unique solution of the inverse problem exists, are formulated in terms of the Weyl function and a procedure to solve the inverse problem is given. The case of the generalized Weyl functions of the form $\phi(\lambda)\exp\{-2i\lambda D\}$, where $\phi$ is a strictly proper rational matrix function and $D=D^* \geq 0$ is a diagonal matrix, is treated in greater detail. Explicit formulas for the inversion of the corresponding semiseparable integral operators and recovery of the Dirac-type system are obtained for this case.

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