Gabriel P. Paternain, Mikko Salo, Gunther Uhlmann

Geometric Inverse Problems (eBook, PDF)

With Emphasis on Two Dimensions

• Format: PDF

Produktbeschreibung

Cutting-edge mathematical tools are used in this treatment of recent developments in geometric inverse problems.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 5. Januar 2023
• Englisch
• ISBN-13: 9781009041423
• Artikelnr.: 70911955

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.