An introduction to inverse scattering and inverse spectral problems /
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| 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: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/12577307 |
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| 050 | 4 | |a QA377 |b .I588 1997eb | |
| 245 | 0 | 3 | |a An introduction to inverse scattering and inverse spectral problems / |c Khosrow Chadan [and others]. |
| 260 | |a Philadelphia, Pa. : |b Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), |c 1997. | ||
| 300 | |a 1 online resource (x, 198 pages) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a SIAM monographs on mathematical modeling and computation ; |v 2 | |
| 500 | |a Title from title screen, viewed 12/30/2010. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a 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. | |
| 520 | 3 | |a 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. | |
| 530 | |a Also available in print version. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Inverse problems (Differential equations) |x Numerical solutions. |0 http://id.loc.gov/authorities/subjects/sh85067685 | |
| 650 | 0 | |a Scattering (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85118046 | |
| 650 | 0 | |a Spectral theory (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85126408 | |
| 650 | 6 | |a Problèmes inverses (Équations différentielles) |x Solutions numériques. | |
| 650 | 6 | |a Dispersion (Mathématiques) | |
| 650 | 6 | |a Spectre (Mathématiques) | |
| 650 | 7 | |a Inverse problems (Differential equations) |x Numerical solutions |2 fast | |
| 650 | 7 | |a Scattering (Mathematics) |2 fast | |
| 650 | 7 | |a Spectral theory (Mathematics) |2 fast | |
| 653 | |a Inverse problems | ||
| 653 | |a Differential equations | ||
| 653 | |a Numerical solutions | ||
| 653 | |a Scattering | ||
| 653 | |a Spectral theory | ||
| 700 | 1 | |a Chadan, K. |q (Khosrow) |0 http://id.loc.gov/authorities/names/n88122885 | |
| 710 | 2 | |a Society for Industrial and Applied Mathematics. |0 http://id.loc.gov/authorities/names/n79053057 | |
| 776 | 0 | 8 | |i Print version: |t Introduction to inverse scattering and inverse spectral problems. |d Philadelphia : Society for Industrial and Applied Mathematics, ©1997 |z 0898713870 |w (DLC) 96052459 |w (OCoLC)36127006 |
| 830 | 0 | |a SIAM monographs on mathematical modeling and computation ; |v 2. |0 http://id.loc.gov/authorities/names/n96115029 | |
| 856 | 4 | 0 | |u https://epubs.siam.org/doi/book/10.1137/1.9780898719710 |y Society for Industrial and Applied Mathematics |
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| 928 | |t Library of Congress classification |a QA377.I588 1997eb |l Online |c UC-FullText |u https://epubs.siam.org/doi/book/10.1137/1.9780898719710 |z Society for Industrial and Applied Mathematics |g ebooks |i 12568691 | ||