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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 monograph deals with inverse problems of spectral analysis for ordinary differential equations and aims to present 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 and opens with the method of spectral mappings, presented in the simplest version for the Sturm-Liouville operator. The second chapter deals with the inverse problem of recovering higher-order differential operators of the form, on the half-line and on a finite interval. In this chapter the author introduces the so-called Weyl matrix, which is a generalization of the classical Weyl function for the selfadjoint second-order differential operator. The last chapter contains a study on inverse spectral problems for differential equations with nonlinear dependence on the spectral parameter.
This monograph will be of value and interest to specialists in the field of inverse problems for differential equations.
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Für höhere Schule und Studium
Für Beruf und Forschung
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ISBN-13
978-90-6764-355-9 (9789067643559)
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Schweitzer Klassifikation
Vyatcheslav A. Yurko, N. G. Chernyshevsky Saratov State University, Russia.
Inverse problems for Sturm-Liouville operators
Sturm-Liouville operators on a finite interval
Uniqueness theorem
Solution of the inverse problem on a finite interval
Sturm-Liouville operators on the half-line
Recovery of Sturm-Liouville operators from the Weyl function
Recovery of Sturm-Liouville operators from the spectral data
Review of the inverse problem theory
Inverse problems for higher-order differential operators
The Weyl matrix. The uniqueness theorem
Solution of the inverse problem on the half-line
Solution of the inverse problem on a finite interval
The selfadjoint case
Differential operators with a separate spectrum
Differential operators with singularities
Inverse problems for pencils of differential operators
Second-order differential equations with nonlinear dependence on the spectral parameter
Regge-type boundary value problems
An inverse problem for differential equations of the Orr-Sommerfeld type
Inverse problems for systems of differential equations
Bibliography
