Levitan B.M. Inverse Sturm-Liouville Problems

Berlin: de Gruyter, 2018. — 252 p.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.transformation operators
inverse sturm-liouville problem on the half-line: determining the sturm-liouville operator from spectral function
determining the regular sturm-liouville operator from two spectra
the inverse problem of the quantum scattering theory
the inverse problem of the quantum scattering theory at fixed energy
the inverse problem of the scattering theory on the whole line
inverse sturm-liouville problem on the whole line from a spectral matrix function
finite-zone potentials
infinite-zone potentials
quasi-periodicity of finite-zone potentials
quasi-periodicity of infinite-zone potentials
relation between the sturm-liouville and the korteweg-de vries equation