The curiosity in inverse difficulties of spectral research has elevated significantly lately as a result of functions to special non-linear equations in mathematical physics. This monograph is dedicated to the specified thought of inverse difficulties and techniques in their answer for the Sturm-Liouville case. Chapters 1--6 comprise proofs that are, in lots of circumstances, very assorted from these identified previous. Chapters 4--6 are dedicated to inverse difficulties of quantum scattering conception with awareness being serious about actual purposes. Chapters 7--11 are in accordance with the author's contemporary study at the idea of finite- and infinite-zone potentials. A bankruptcy discussing the functions to the Korteweg--de Vries challenge is additionally incorporated. This monograph is critical interpreting for all researchers within the box of arithmetic and physics.
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