An introduction to inverse scattering and inverse spectral problems:
Gespeichert in:
| Format: | Elektronisch E-Book |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Philadelphia, Pa.
Society for Industrial and Applied Mathematics
1997
|
| Schriftenreihe: | SIAM monographs on mathematical modeling and computation
2 |
| Schlagworte: | |
| Online-Zugang: | TUM01 UBW01 UBY01 UER01 Volltext |
| Beschreibung: | Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references and index 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 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 |
| Beschreibung: | 1 Online-Ressource (x, 198 Seiten) |
| ISBN: | 0898713870 9780898713879 |
| DOI: | 10.1137/1.9780898719710 |
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| 500 | |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 | ||
| 500 | |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 | ||
| 650 | 4 | |a Inverse problems (Differential equations) / Numerical solutions | |
| 650 | 4 | |a Scattering (Mathematics) | |
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| id | DE-604.BV039747136 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:10:18Z |
| institution | BVB |
| isbn | 0898713870 9780898713879 |
| language | English |
| lccn | 96052459 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024594666 |
| oclc_num | 873886120 |
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| owner_facet | DE-91 DE-BY-TUM DE-29 DE-706 DE-83 DE-20 |
| physical | 1 Online-Ressource (x, 198 Seiten) |
| psigel | ZDB-72-SIA |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | marc |
| series | SIAM monographs on mathematical modeling and computation |
| series2 | SIAM monographs on mathematical modeling and computation |
| spelling | An introduction to inverse scattering and inverse spectral problems Khosrow Chadan; David Colton ; Lassi Päivärinta ; William Rundell Philadelphia, Pa. Society for Industrial and Applied Mathematics 1997 1 Online-Ressource (x, 198 Seiten) txt rdacontent c rdamedia cr rdacarrier SIAM monographs on mathematical modeling and computation 2 Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references and index 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 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 Inverse problems (Differential equations) / Numerical solutions Scattering (Mathematics) Spectral theory (Mathematics) Inverse Spektraltheorie (DE-588)4314037-3 gnd rswk-swf Inverse Spektraltheorie (DE-588)4314037-3 s DE-604 Chadan, Khosrow Sonstige oth Colton, David 1943- Sonstige (DE-588)115774173 oth Päivärinta, Lassi Sonstige oth Rundell, William Sonstige oth Erscheint auch als Druck-Ausgabe, Paperback 0898713870 Erscheint auch als Druck-Ausgabe, Paperback 9780898713879 SIAM monographs on mathematical modeling and computation 2 (DE-604)BV047220660 2 https://doi.org/10.1137/1.9780898719710 Verlag Volltext |
| spellingShingle | An introduction to inverse scattering and inverse spectral problems SIAM monographs on mathematical modeling and computation Inverse problems (Differential equations) / Numerical solutions Scattering (Mathematics) Spectral theory (Mathematics) Inverse Spektraltheorie (DE-588)4314037-3 gnd |
| subject_GND | (DE-588)4314037-3 |
| title | An introduction to inverse scattering and inverse spectral problems |
| title_auth | An introduction to inverse scattering and inverse spectral problems |
| title_exact_search | An introduction to inverse scattering and inverse spectral problems |
| title_full | An introduction to inverse scattering and inverse spectral problems Khosrow Chadan; David Colton ; Lassi Päivärinta ; William Rundell |
| title_fullStr | An introduction to inverse scattering and inverse spectral problems Khosrow Chadan; David Colton ; Lassi Päivärinta ; William Rundell |
| title_full_unstemmed | An introduction to inverse scattering and inverse spectral problems Khosrow Chadan; David Colton ; Lassi Päivärinta ; William Rundell |
| title_short | An introduction to inverse scattering and inverse spectral problems |
| title_sort | an introduction to inverse scattering and inverse spectral problems |
| topic | Inverse problems (Differential equations) / Numerical solutions Scattering (Mathematics) Spectral theory (Mathematics) Inverse Spektraltheorie (DE-588)4314037-3 gnd |
| topic_facet | Inverse problems (Differential equations) / Numerical solutions Scattering (Mathematics) Spectral theory (Mathematics) Inverse Spektraltheorie |
| url | https://doi.org/10.1137/1.9780898719710 |
| volume_link | (DE-604)BV047220660 |
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