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The inverse problem for the Sturm- Liouville operator with complex periodicpotential and positive discontinuous coefficients on the axis is studied. Maincharacteristics of the fundamental solutions are investigated, the spectrum ofthe operator is studied. We give formulation of the inverse problem, prove auniqueness theorem and provide a constructive procedure for the solution of theinverse problem

The One-Dimenshional Inverse Wave Spectral Problem with Discontinuous Wave Speed