Softcover ISBN:  9780821837559 
Product Code:  CONM/405 
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Electronic ISBN:  9780821879955 
Product Code:  CONM/405.E 
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Book DetailsContemporary MathematicsVolume: 405; 2006; 155 ppMSC: 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 crossdisciplinary 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.ReadershipGraduate students and research mathematicians interested in real analysis, integral geometry, and tomography.

Table of Contents

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 PaleyWiener functions on Riemannian manifolds [ MR 2239176 ]

Jillian Rennie  Properties of the stationary sets for the wave equation [ MR 2239177 ]


Additional Material

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 wellwritten 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


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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 crossdisciplinary 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 PaleyWiener 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 wellwritten 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