Geometric Inverse Problems - Paternain, Gabriel P

. .

Résumé :
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.

Biographie:
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.

Sommaire:
Foreword Andr?s 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 dollarsI^{*}_{0} dollars; 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.