Gabriel P. Paternain (University of Cambridge), Mikko Salo (Finland University of Jyvaskyla), Gunther Uhlmann (University of Washington)

Geometric Inverse Problems

With Emphasis on Two Dimensions

• Gebundenes Buch

Produktbeschreibung

This self-contained treatment of recent developments in geometric inverse problems caters to graduate students and researchers working in inverse problems, differential geometry and microlocal analysis. Many exercises and examples, as well as background material, make it an excellent self-study resource or text for a one-semester course or seminar.

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Produktdetails

• Cambridge Studies in Advanced Mathematics
• Verlag: Cambridge University Press
• Seitenzahl: 350
• Erscheinungstermin: 5. Januar 2023
• Englisch
• Abmessung: 227mm x 158mm x 30mm
• Gewicht: 704g
• ISBN-13: 9781316510872
• ISBN-10: 1316510875
• Artikelnr.: 65688546

Autorenporträt

Gabriel P. Paternain is Professor of Mathematics at the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge and a Fellow of Trinity College. His research has covered an ample mathematical landscape, including Hamiltonian dynamics, symplectic geometry and geometric inverse problems. He is the author of the monograph 'Geodesic Flows' (1999), and was awarded the Pilkington Teaching Prize at Cambridge for his ability to explain analysis and geometry with a clarity that has won him the admiration and respect of his students.

Inhaltsangabe

Foreword András Vasy
Preface
1. The Radon transform in the plane
2. Radial sound speeds
3. Geometric preliminaries
4. The geodesic X-ray transform
5. Regularity results for the transport equation
6. Vertical Fourier analysis
7. The X-ray transform in non-positive curvature
8. Microlocal aspects, surjectivity of $I^{*}_{0}$
9. Inversion formulas and range
10. Tensor tomography
11. Boundary rigidity
12. The attenuated geodesic X-ray transform
13. Non-Abelian X-ray transforms
14. Non-Abelian X-ray transforms II
15. Open problems and related topics
References
Index.