Method of Spectral Mappings in the Inverse Problem Theory

Inverse problems of spectral analysis consist in recovering operators from their spectral characteristics. Such problems often appear in mathematics, mechanics, physics, electronics, geophysics, meteorology and other branches of natural science.

This monographis devoted to inverse problems of spectral analysis for ordinary differential equations. Its aim ist topresent the main results on inverse spectral problems using the so-called method of spectral mappings, which is one of the main tools in inverse spectral theory.

The book consists of three chapters: In Chapter1the method of spectral mappings ispresented in the simplest version for the Sturm-Liouville operator. In Chapter 2the inverse problem of recovering higher-order differential operators of the form, on the half-line and on a finite interval, is considered. In Chapter 3inverse spectral problems for differential operators with nonlinear dependence on the spectral parameter are studied.