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Cambridge Studies in Advanced Mathematics Ser.: Geometric Inverse Problems : With Emphasis on Two Dimensions by Gabriel P. Paternain, Mikko Salo and Gunther Uhlmann (2023, Hardcover)
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Geometric Inverse Problems : With Emphasis on Two Dimensions, Hardcover by Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther, ISBN 1316510875, ISBN-13 9781316510872, Brand New, Free shipping in the US
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About this product
Product Identifiers
PublisherCambridge University Press
ISBN-101316510875
ISBN-139781316510872
eBay Product ID (ePID)25057255719
Product Key Features
Number of Pages350 Pages
Publication NameGeometric Inverse Problems : with Emphasis on Two Dimensions
LanguageEnglish
Publication Year2023
SubjectGeometry / General, General
TypeTextbook
AuthorGabriel P. Paternain, Mikko Salo, Gunther Uhlmann
Subject AreaMathematics
SeriesCambridge Studies in Advanced Mathematics Ser.
FormatHardcover
Dimensions
Item Height1.1 in
Item Length9.3 in
Item Width6.2 in
Additional Product Features
LCCN2022-030681
Reviews'This monograph gives a beautiful introduction to Geometric inverse problems, largely in dimension two, by three of the most prominent contributors to the field. The Geometric problems are interesting as pure mathematics, but they also arise from applications to tomography, such as the Calderon problem of determining (M, g) from its Dirichlet-to-Neumann map. Roughly speaking, the underlying physics problem is to determine electrical properties of a medium by making voltage and current measurements on the boundary. Techniques of microlocal analysis relate such PDE boundary inverse problems to geometric inverse problems. These inverse problems furnish problems of great interest in PDE and in geometry in a rather concrete setting, and are masterfully conveyed by the authors. The level is appropriate for a graduate class in mathematics but is also an excellent entrée into the field for research mathematicians.' Steve Zelditch, Northwestern University
Dewey Edition23
Series Volume NumberSeries Number 204
IllustratedYes
Dewey Decimal515.357
Table Of ContentForeword 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.
SynopsisThis 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., 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.
LC Classification NumberQA378.5.P38 2023
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