Inverse Sturm-Liouville Problems

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. Contents Preface Introduction Chapter 1. transformation operators Chapter 2. inverse sturm-liouville problem on the half-line: determining the sturm-liouville operator from spectral function Chapter 3. determining the regular sturm-liouville operator from two spectra Chapter 4. the inverse problem of the quantum scattering theory Chapter 5. the inverse problem of the quantum scattering theory at fixed energy Chapter 6. the inverse problem of the scattering theory on the whole line Chapter 7. inverse sturm-liouville problem on the whole line from a spectral matrix function Chapter 8. finite-zone potentials Chapter 9. infinite-zone potentials Chapter 10. quasi-periodicity of finite-zone potentials Chapter 11. quasi-periodicity of infinite-zone potentials Chapter 12. relation between the sturm-liouville and the kortewegde vries equation References

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