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03262aam a2200397 i 4500 001 591778127A0E11EE96FE52224AECA4DB 003 SILO 005 20231103010033 008 220819t20232023enka b 001 0 eng 010 $a 2022030681 020 $a 1316510875 020 $a 9781316510872 035 $a (OCoLC)1342490656 040 $a LBSOR/DLC $b eng $e rda $c DLC $d OCLCF $d UKMGB $d IPS $d HUL $d CGU $d YDX $d SILO 042 $a pcc 050 00 $a QA378.5 P38 2023 100 1 $a Paternain, Gabriel P. $q (Gabriel Pedro), $d 1964- $e author. 245 10 $a Geometric inverse problems : $b with emphasis on two dimensions / $c Gabriel P. Paternain, Mikko Salo, Gunther Uhlmann. 246 3 $a With emphasis on 2 dimensions 264 1 $a Cambridge, United Kingdom ; $b Cambridge University Press, $c 2023. 300 $a xxiv, 344 pages : $b illustrations ; $c 24 cm 490 1 $a Cambridge studies in advanced mathematics ; $v 204 504 $a Includes bibliographical references and index. 505 0 $a 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. 520 $a "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 CalderoÌn 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"-- $c Provided by publisher. 650 0 $a Inverse problems (Differential equations) 650 0 $a Inversions (Geometry) 650 0 $a Geometry, Differential. 700 1 $a Salo, Mikko, $e author. 700 1 $a Uhlmann, Gunther, $d 1952- $e author. 776 08 $i Online version: $a Paternain, Gabriel P. (Gabriel Pedro), 1964- $t Geometric inverse problems $d Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2023 $z 9781009039901 $w (DLC) 2022030682 830 0 $a Cambridge studies in advanced mathematics ; $v 204. 941 $a 1 952 $l USUX851 $d 20240202024924.0 956 $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=591778127A0E11EE96FE52224AECA4DB 994 $a C0 $b IWAInitiate Another SILO Locator Search