An introduction to inverse scattering and inverse spectral problems / Khosrow Chadan ... [et al.].

Format:

Book

Contributor:

Chadan, K. (Khosrow)

Society for Industrial and Applied Mathematics.

Series:

SIAM monographs on mathematical modeling and computation ; 2.

SIAM monographs on mathematical modeling and computation ; 2

Language:

English

Subjects (All):

Inverse problems (Differential equations)--Numerical solutions.

Scattering (Mathematics).

Spectral theory (Mathematics).

Physical Description:

1 electronic text (x, 198 p.) : ill., digital file.

Place of Publication:

Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1997.

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

Here is a clearly written introduction to three central areas of inverse problems: inverse problems in electromagnetic scattering theory, inverse spectral theory, and inverse problems in quantum scattering theory. Inverse problems, one of the most attractive parts of applied mathematics, attempt to obtain information about structures by nondestructive measurements. Based on a series of lectures presented by three of the authors, all experts in the field, the book provides a quick and easy way for readers to become familiar with the area through a survey of recent developments in inverse spectral and inverse scattering problems.

Contents:

Foreword

Preface

1. A Review of basic mathematical tools / Lassi Päivärinta

Linear operators on Hilbert space

Integral operators and the Fredholm alternative

The Fourier transform and the Hilbert transform

The unique continuation principle (UCP)

Unbounded operators

The spectrum

The resolvent kernel and the Fredholm determinant

A particle in a box

Maxwell's equations

References

2. Multidimensional inverse scattering theory / David Colton

Electromagnetic scattering problem

Bessel functions

The addition formula

Green's formula

Basic properties of far field patterns

Spectral theory of the far field operator

The inverse scattering problem

The detection and monitoring of leukemia

Regularization

Closing remarks

3. Inverse Sturm-Liouville problems / William Rundell

Introduction

Preliminary material

The Liouville transformation

Asymptotic expansions of the eigenvalues and eigenfunctions

The inverse problem, a historical look

A completeness result

An important integral operator

Solving hyperbolic equations

Uniqueness proofs

Constructive algorithms

Modification for other spectral data

Other differential equations

Other constructive algorithms

The matrix analogue

Another finite-dimensional algorithm

Fourth-order problems

4. Inverse problems in potential scattering / Khosrow Chadan

Physical background and formulation of the inverse scattering problem

Scattering theory for partial waves

Gel'fand-Levitan integral equation

Marchenko equation

Inverse problem on the line

Nonlinear evolution equations

Appendix

Index.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Title from title screen, viewed 12/30/2010.

ISBN:

0-89871-971-2

Publisher Number:

MM02 SIAM