Non-self-adjoint second-order differential operators on a finite interval with indefinite discontinuous weights are studied. Properties of spectral characteristics are established and inverse problems of recovering operators from their spectral characteristics are investigated. For these class of nonlinear inverse problems algorithms for constructing the global solutions are developed, and uniqueness theorems are proved.

中文翻译：

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具有不连续权重的微分算子的反问题

研究了权重不连续的有限区间上的非自伴随二阶微分算子。建立了频谱特性的性质，研究了从频谱特性恢复算子的逆问题。针对这类非线性逆问题，开发了构建全局解的算法，并证明了唯一性定理。