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Non-self-adjoint second-order differential pencils on a finite interval withnon-separated quasi-periodic boundary conditions and jump conditions arestudied. We establish properties of spectral characteristics and investigatethe inverse spectral problem of recovering the operator from its spectral data.For this inverse problem we prove the corresponding uniqueness theorem andprovide an algorithm for constructing its solution.

On Quasi-periodic Differential Pencils with Jump Conditions Inside the Interval