Inverse Sturm-Liouville Problems

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The interest in inverse problems of spectral analysis has increased considerably in recent years due to the applications to important non-linear equations in mathematical physics.
This monograph is devoted to the detailed theory of inverse problems and methods of their solution for the Sturm-Liouville case.
Chapters 1–6 contain proofs which are, in many cases, very different from those known earlier. Chapters 4–6 are devoted to inverse problems of quantum scattering theory with attention being focused on physical applications. Chapters 7–11 are based on the author’s recent research on the theory of finite- and infinite-zone potentials. A chapter discussing the applications to the Korteweg–de Vries problem is also included. This monograph is important reading for all researchers in the field of mathematics and physics.