Singularities of Jost functions and potentials

The possibility of determining a potential from given singularities of Jost functions is investigated. It is proved that forN poles the problem can be reduced to the solving of a system ofN linear nonhomogeneous equations and in the case of discontinuities along a cut to the solving of a nonhomogeneous integral equation. The obtained potentials are a superposition of exponential potentials.

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