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Integral Geometry and Tomography

Edited by: Andrew Markoe Rider University, Lawrenceville, NJ
Eric Todd Quinto Tufts University, Medford, MA
Available Formats:
Softcover ISBN: 978-0-8218-3755-9
Product Code: CONM/405
List Price: $69.00 MAA Member Price:$62.10
AMS Member Price: $55.20 Electronic ISBN: 978-0-8218-7995-5 Product Code: CONM/405.E List Price:$65.00
MAA Member Price: $58.50 AMS Member Price:$52.00
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $103.50 MAA Member Price:$93.15
AMS Member Price: $82.80 Click above image for expanded view Integral Geometry and Tomography Edited by: Andrew Markoe Rider University, Lawrenceville, NJ Eric Todd Quinto Tufts University, Medford, MA Available Formats:  Softcover ISBN: 978-0-8218-3755-9 Product Code: CONM/405  List Price:$69.00 MAA Member Price: $62.10 AMS Member Price:$55.20
 Electronic ISBN: 978-0-8218-7995-5 Product Code: CONM/405.E
 List Price: $65.00 MAA Member Price:$58.50 AMS Member Price: $52.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$103.50 MAA Member Price: $93.15 AMS Member Price:$82.80
• Book Details

Contemporary Mathematics
Volume: 4052006; 155 pp
MSC: Primary 44; 92; Secondary 35; 42; 43; 52; 94;

This volume consists of a collection of papers that brings together fundamental research in Radon transforms, integral geometry, and tomography. It grew out of the Special Session at a Sectional Meeting of the American Mathematical Society in 2004. The book contains very recent work of some of the top researchers in the field.

The articles in the book deal with the determination of properties of functions on a manifold by integral theoretic methods, or by determining the geometric structure of subsets of a manifold by analytic methods. Of particular concern are ways of reconstructing an unknown function from some of its projections.

Radon transforms were developed at the beginning of the twentieth century by researchers who were motivated by problems in differential geometry, mathematical physics, and partial differential equations. Later, medical applications of these transforms produced breakthroughs in imaging technology that resulted in the 1979 Nobel Prize in Physiology and Medicine for the development of computerized tomography. Today the subject boasts substantial cross-disciplinary interactions, both in pure and applied mathematics as well as medicine, engineering, biology, physics, geosciences, and industrial testing. Therefore, this volume should be of interest to a wide spectrum of researchers both in mathematics and in other fields.

Graduate students and research mathematicians interested in real analysis, integral geometry, and tomography.

• Articles
• Mark L. Agranovsky and Eric Todd Quinto - Remarks on stationary sets for the wave equation [ MR 2239167 ]
• Carlos Berenstein, Franklin Gavilánez and John Baras - Network tomography [ MR 2239168 ]
• Jan Boman - On stable inversion of the attenuated Radon transform with half data [ MR 2239169 ]
• Mihaela Dobrescu and Gestur Ólafsson - Wavelet sets without groups [ MR 2239170 ]
• Leon Ehrenpreis - The Radon transform for functions defined on planes [ MR 2239171 ]
• Fulton B. Gonzalez and Jingjin Zhang - The modified wave equation on the sphere [ MR 2239172 ]
• A. Katsevich and A. Zamyatin - Analysis of a family of exact inversion formulas for cone beam computer tomography [ MR 2239173 ]
• Andrew Markoe - The $k$-plane transform and Riesz potentials [ MR 2239174 ]
• E. Ournycheva and B. Rubin - The composite cosine transform on the Stiefel manifold and generalized zeta integrals [ MR 2239175 ]
• Isaac Pesenson - Frames for spaces of Paley-Wiener functions on Riemannian manifolds [ MR 2239176 ]
• Jillian Rennie - Properties of the stationary sets for the wave equation [ MR 2239177 ]

• Reviews

• Important and commendable ... Students fortunate enough to read and digest them will be exposed to a consistent, entertaining, and stimulatingly rich study, immensely suggestive, well researched, and intellectually appealing in their scholarly approach. Rarely do books meet such high aspirations, yet this one certainly does. All of the papers are consistently well-written by the most active and highly regarded researchers in the field, and promise to serve as a valuable reference source for many years to come.

Current Engineering Practice
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 4052006; 155 pp
MSC: Primary 44; 92; Secondary 35; 42; 43; 52; 94;

This volume consists of a collection of papers that brings together fundamental research in Radon transforms, integral geometry, and tomography. It grew out of the Special Session at a Sectional Meeting of the American Mathematical Society in 2004. The book contains very recent work of some of the top researchers in the field.

The articles in the book deal with the determination of properties of functions on a manifold by integral theoretic methods, or by determining the geometric structure of subsets of a manifold by analytic methods. Of particular concern are ways of reconstructing an unknown function from some of its projections.

Radon transforms were developed at the beginning of the twentieth century by researchers who were motivated by problems in differential geometry, mathematical physics, and partial differential equations. Later, medical applications of these transforms produced breakthroughs in imaging technology that resulted in the 1979 Nobel Prize in Physiology and Medicine for the development of computerized tomography. Today the subject boasts substantial cross-disciplinary interactions, both in pure and applied mathematics as well as medicine, engineering, biology, physics, geosciences, and industrial testing. Therefore, this volume should be of interest to a wide spectrum of researchers both in mathematics and in other fields.

Graduate students and research mathematicians interested in real analysis, integral geometry, and tomography.

• Articles
• Mark L. Agranovsky and Eric Todd Quinto - Remarks on stationary sets for the wave equation [ MR 2239167 ]
• Carlos Berenstein, Franklin Gavilánez and John Baras - Network tomography [ MR 2239168 ]
• Jan Boman - On stable inversion of the attenuated Radon transform with half data [ MR 2239169 ]
• Mihaela Dobrescu and Gestur Ólafsson - Wavelet sets without groups [ MR 2239170 ]
• Leon Ehrenpreis - The Radon transform for functions defined on planes [ MR 2239171 ]
• Fulton B. Gonzalez and Jingjin Zhang - The modified wave equation on the sphere [ MR 2239172 ]
• A. Katsevich and A. Zamyatin - Analysis of a family of exact inversion formulas for cone beam computer tomography [ MR 2239173 ]
• Andrew Markoe - The $k$-plane transform and Riesz potentials [ MR 2239174 ]
• E. Ournycheva and B. Rubin - The composite cosine transform on the Stiefel manifold and generalized zeta integrals [ MR 2239175 ]
• Isaac Pesenson - Frames for spaces of Paley-Wiener functions on Riemannian manifolds [ MR 2239176 ]
• Jillian Rennie - Properties of the stationary sets for the wave equation [ MR 2239177 ]
• Important and commendable ... Students fortunate enough to read and digest them will be exposed to a consistent, entertaining, and stimulatingly rich study, immensely suggestive, well researched, and intellectually appealing in their scholarly approach. Rarely do books meet such high aspirations, yet this one certainly does. All of the papers are consistently well-written by the most active and highly regarded researchers in the field, and promise to serve as a valuable reference source for many years to come.

Current Engineering Practice
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.