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Geometric Inverse Problems - With Emphasis on Two Dimensions (Hardcover)
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Geometric Inverse Problems - With Emphasis on Two Dimensions (Hardcover)
Series: Cambridge Studies in Advanced Mathematics
Expected to ship within 12 - 17 working days
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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
Calderon 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.
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