Method of Spectral Mappings in the Inverse Problem Theory
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Method of Spectral Mappings in the Inverse Problem Theory

Method of Spectral Mappings in the Inverse Problem Theory

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About the Book

01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information. 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.

Table of Contents:
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


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Product Details
  • ISBN-13: 9789067643559
  • Publisher: Brill
  • Publisher Imprint: VSP International Science Publishers
  • Language: English
  • Weight: 640 gr
  • ISBN-10: 9067643556
  • Publisher Date: 01 Jan 2002
  • Binding: Hardback
  • No of Pages: 304


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