An introduction to inverse scattering and inverse spectral problems /

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Bibliographic Details
Imprint:	Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1997.
Description:	1 online resource (x, 198 pages) : illustrations.
Language:	English
Series:	SIAM monographs on mathematical modeling and computation ; 2 SIAM monographs on mathematical modeling and computation ; 2.
Subject:	Inverse problems (Differential equations) -- Numerical solutions. Scattering (Mathematics) Spectral theory (Mathematics) Inverse problems (Differential equations) -- Numerical solutions Scattering (Mathematics) Spectral theory (Mathematics)
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/12577307

Hidden Bibliographic Details
Other authors / contributors:	Chadan, K. (Khosrow) Society for Industrial and Applied Mathematics.
ISBN:	9780898719710 0898719712 9780898713879 0898713870
Notes:	Title from title screen, viewed 12/30/2010. Includes bibliographical references and index. Also available in print version. English.
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.
Other form:	Print version: Introduction to inverse scattering and inverse spectral problems. Philadelphia : Society for Industrial and Applied Mathematics, ©1997 0898713870
Publisher's no.:	MM02 SIAM

Table of 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
References
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
References
4. Inverse problems in potential scattering / Khosrow Chadan
Introduction
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
Closing remarks
Appendix
References
Index.

An introduction to inverse scattering and inverse spectral problems /

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