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Method of Spectral Mappings in the Inverse Problem Theory
V. A. Yurko
出版VSP, 2002-01-01
主題Mathematics / Geometry / GeneralMathematics / Differential Equations / General
ISBN97890676435599067643556
URLhttp://books.google.com.hk/books?id=c7z0nxi7HLAC&hl=&source=gbs_api
EBookSAMPLE
註釋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.