Geometric inverse problems : with emphasis on two dimensions / Gabriel P. Paternain, Mikko Salo, Gunther Uhlmann.

Format:

Book

Author/Creator:

Paternain, Gabriel P. (Gabriel Pedro), 1964- author.

Salo, Mikko, author.

Uhlmann, Gunther, 1952- author.

Series:

Cambridge studies in advanced mathematics ; 204.

Cambridge studies in advanced mathematics, 0950-6330 ; 204

Language:

English

Subjects (All):

Inverse problems (Differential equations).

Inversions (Geometry).

Geometry, Differential.

Physical Description:

xxiv, 344 pages : illustrations ; 24 cm.

Other Title:

With emphasis on 2 dimensions

Place of Publication:

Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2023.

Summary:

"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"-- Provided by publisher.

Contents:

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.

Notes:

Includes bibliographical references and index.

Other Format:

Online version: Paternain, Gabriel P. (Gabriel Pedro), 1964- Geometric inverse problems

ISBN:

9781316510872

1316510875

OCLC:

1342490656