Contemporary Mathematics
Volume: 405;
2006;
155 pp;
Softcover
MSC: Primary 44; 92;
Secondary 35; 42; 43; 52; 94
Print ISBN: 978-0-8218-3755-9
Product Code: CONM/405
List Price: $65.00
AMS Member Price: $52.00
MAA Member Price: $58.50
Electronic ISBN: 978-0-8218-7995-5
Product Code: CONM/405.E
List Price: $65.00
AMS Member Price: $52.00
MAA Member Price: $58.50
Integral Geometry and Tomography
Share this pageEdited by Andrew Markoe; Eric Todd Quinto
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.
Readership
Graduate students and research mathematicians interested in real analysis, integral geometry, and tomography.
Reviews & Endorsements
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
Table of Contents
Integral Geometry and Tomography
- Preface vii8 free
- Remarks on Stationary Sets for the Wave Equation 118 free
- Network Tomography 1128
- On Stable Inversion of the Attenuated Radon Transform with Half Data 1936
- Wavelet Sets Without Groups 2744
- The Radon Transform for Functions Defined on Planes 4158
- Analysis of a Family of Exact Inversion Formulas for Cone Beam Computer Tomography 5976
- The k-Plane Transform and Riesz Potentials 7592
- The Composite Cosine Transform on the Stiefel Manifold and Generalized Zeta Integrals 111128
- Frames for Spaces of Paley-Wiener Functions on Riemannian Manifolds 135152
- Properties of the Stationary Sets for the Wave Equation 149166