Geometric inverse problems : with emphasis on two dimensions /
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| Author / Creator: | Paternain, Gabriel P. (Gabriel Pedro), 1964- author. |
|---|---|
| Imprint: | Cambridge ; New York, NY : Cambridge University Press, 2023. |
| Description: | xxiv, 344 pages : illustrations ; 24cm. |
| Language: | English |
| Series: | Cambridge studies in advanced mathematics, 0950-6330 ; 204 Cambridge studies in advanced mathematics ; 204. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/13124362 |
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| 029 | 1 | |a UKMGB |b 020807772 | |
| 035 | |a (OCoLC)1342490656 | ||
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| 050 | 0 | 0 | |a QA378.5 |b .P38 2023 |
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| 100 | 1 | |a Paternain, Gabriel P. |q (Gabriel Pedro), |d 1964- |e author. | |
| 245 | 1 | 0 | |a Geometric inverse problems : |b with emphasis on two dimensions / |c Gabriel P. Paternain, Mikko Salo, Gunther Uhlmann. |
| 264 | 1 | |a Cambridge ; |a New York, NY : |b Cambridge University Press, |c 2023. | |
| 300 | |a xxiv, 344 pages : |b illustrations ; |c 24cm. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a unmediated |b n |2 rdamedia | ||
| 338 | |a volume |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge studies in advanced mathematics, |x 0950-6330 ; |v 204 | |
| 500 | |a Foreward by András Vasy. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a The Radon transform in the plane -- Radial sound speeds -- Geometric preliminaries -- The geodesic X-ray transform -- Regularity results for the transport equation -- Vertical Fourier analysis -- The X-ray transform in non-positive curvature -- Microlocal aspects, surjectivity of I*0 -- Inversion formulas and range -- Tensor tomography -- Boundary rigidity -- The attenuated geodesic X-ray transform -- Non-Abelian X-ray transforms -- Non-Abelian X-ray transforms II -- Open problems and related topics. | |
| 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 section discusses current open problems and related topics. The numerous exercises and examples make this book an excellent self-study resource or text for a onesemester course or seminar"-- |c Provided by publisher. | ||
| 650 | 0 | |a Inverse problems (Differential equations) | |
| 650 | 0 | |a Inversions (Geometry) | |
| 650 | 0 | |a Geometry, Differential. | |
| 650 | 7 | |a Geometry, Differential. |2 fast |0 (OCoLC)fst00940919 | |
| 650 | 7 | |a Inverse problems (Differential equations) |2 fast |0 (OCoLC)fst00978098 | |
| 650 | 7 | |a Inversions (Geometry) |2 fast |0 (OCoLC)fst00978104 | |
| 700 | 1 | |a Salo, Mikko, |e author. | |
| 700 | 1 | |a Uhlmann, Gunther, |d 1952- |e author. | |
| 830 | 0 | |a Cambridge studies in advanced mathematics ; |v 204. | |
| 929 | |a cat | ||
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| 928 | |t Library of Congress classification |a QA378.5.P38 2023 |l Eck |c Eck-Eck |i 13263929 | ||
| 927 | |t Library of Congress classification |a QA378.5.P38 2023 |l Eck |c Eck-Eck |g SEPS |b 118441033 |i 10492949 | ||