Geometric inverse problems: with emphasis on two dimensions
This up-to-date treatment of recent developments in geometric inverse problems introduces graduate students and researchers to an exciting area of research. With an emphasis on the two-dimensional case, topics covered include geodesic X-ray transforms, boundary rigidity, tensor tomography, attenuate...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2023
|
| Schriftenreihe: | Cambridge studies in advanced mathematics
204 |
| Schlagworte: | |
| Online-Zugang: | DE-12 DE-634 DE-92 DE-91 Volltext |
| Zusammenfassung: | This up-to-date treatment of recent developments in geometric inverse problems introduces graduate students and researchers to an exciting area of research. With an emphasis on the two-dimensional case, topics covered include geodesic X-ray transforms, boundary rigidity, tensor tomography, attenuated X-ray transforms and the Calderón problem. The presentation is self-contained and begins with the Radon transform and radial sound speeds as motivating examples. The required geometric background is developed in detail in the context of simple manifolds with boundary. An in-depth analysis of various geodesic X-ray transforms is carried out together with related uniqueness, stability, reconstruction and range characterization results. Highlights include a proof of boundary rigidity for simple surfaces as well as scattering rigidity for connections. The concluding chapter discusses current open problems and related topics. The numerous exercises and examples make this book an excellent self-study resource or text for a one-semester course or seminar. |
| Beschreibung: | 1 Online-Ressource (xxiv, 344 Seiten) |
| ISBN: | 9781009039901 |
| DOI: | 10.1017/9781009039901 |
Internformat
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| 490 | 1 | |a Cambridge studies in advanced mathematics |v 204 | |
| 520 | |a This up-to-date treatment of recent developments in geometric inverse problems introduces graduate students and researchers to an exciting area of research. With an emphasis on the two-dimensional case, topics covered include geodesic X-ray transforms, boundary rigidity, tensor tomography, attenuated X-ray transforms and the Calderón problem. The presentation is self-contained and begins with the Radon transform and radial sound speeds as motivating examples. The required geometric background is developed in detail in the context of simple manifolds with boundary. An in-depth analysis of various geodesic X-ray transforms is carried out together with related uniqueness, stability, reconstruction and range characterization results. Highlights include a proof of boundary rigidity for simple surfaces as well as scattering rigidity for connections. The concluding chapter discusses current open problems and related topics. The numerous exercises and examples make this book an excellent self-study resource or text for a one-semester course or seminar. | ||
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| isbn | 9781009039901 |
| language | English |
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| spelling | Paternain, Gabriel P. 1964- (DE-588)121598888 aut Geometric inverse problems with emphasis on two dimensions Gabriel P. Paternain, Mikko Salo, Gunther Uhlmann Cambridge Cambridge University Press 2023 1 Online-Ressource (xxiv, 344 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 204 This up-to-date treatment of recent developments in geometric inverse problems introduces graduate students and researchers to an exciting area of research. With an emphasis on the two-dimensional case, topics covered include geodesic X-ray transforms, boundary rigidity, tensor tomography, attenuated X-ray transforms and the Calderón problem. The presentation is self-contained and begins with the Radon transform and radial sound speeds as motivating examples. The required geometric background is developed in detail in the context of simple manifolds with boundary. An in-depth analysis of various geodesic X-ray transforms is carried out together with related uniqueness, stability, reconstruction and range characterization results. Highlights include a proof of boundary rigidity for simple surfaces as well as scattering rigidity for connections. The concluding chapter discusses current open problems and related topics. The numerous exercises and examples make this book an excellent self-study resource or text for a one-semester course or seminar. Inverse problems (Differential equations) Inversions (Geometry) Geometry, Differential Salo, Mikko 1979- (DE-588)173729959 aut Uhlmann, Gunther 1952- (DE-588)1044043687 aut Erscheint auch als Druck-Ausgabe 978-1-31-651087-2 Cambridge studies in advanced mathematics 204 (DE-604)BV044781283 204 https://doi.org/10.1017/9781009039901 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Paternain, Gabriel P. 1964- Salo, Mikko 1979- Uhlmann, Gunther 1952- Geometric inverse problems with emphasis on two dimensions Inverse problems (Differential equations) Inversions (Geometry) Geometry, Differential Cambridge studies in advanced mathematics |
| title | Geometric inverse problems with emphasis on two dimensions |
| title_auth | Geometric inverse problems with emphasis on two dimensions |
| title_exact_search | Geometric inverse problems with emphasis on two dimensions |
| title_exact_search_txtP | Geometric inverse problems with emphasis on two dimensions |
| title_full | Geometric inverse problems with emphasis on two dimensions Gabriel P. Paternain, Mikko Salo, Gunther Uhlmann |
| title_fullStr | Geometric inverse problems with emphasis on two dimensions Gabriel P. Paternain, Mikko Salo, Gunther Uhlmann |
| title_full_unstemmed | Geometric inverse problems with emphasis on two dimensions Gabriel P. Paternain, Mikko Salo, Gunther Uhlmann |
| title_short | Geometric inverse problems |
| title_sort | geometric inverse problems with emphasis on two dimensions |
| title_sub | with emphasis on two dimensions |
| topic | Inverse problems (Differential equations) Inversions (Geometry) Geometry, Differential |
| topic_facet | Inverse problems (Differential equations) Inversions (Geometry) Geometry, Differential |
| url | https://doi.org/10.1017/9781009039901 |
| volume_link | (DE-604)BV044781283 |
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