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Integral Geometry and Tomography
Edited by: Eric Grinberg and Eric Todd Quinto
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Contemporary Mathematics
1991; 251 pp; softcover
Volume: 113
ISBN-10: 0-8218-5120-9
ISBN-13: 978-0-8218-5120-3
List Price: US$68
Member Price: US$54.40
Order Code: CONM/113
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This book contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Integral Geometry and Tomography, held in June 1989 at Humboldt State University in Arcata, California. The papers collected here represent current research in these two interrelated fields. The articles in pure mathematics range over such diverse areas as combinatorics, geometric inequalities, micro-local analysis, group theory, and harmonic analysis. The interplay between Lie group theory, geometry, harmonic analysis, and Radon transforms is well covered. The papers on tomography reflect current research on X-ray computed tomography, as well as radiation dose planning, radar, and partial differential equations.

In addition to describing current research, this book provides a useful perspective on the interplay between the fields. For example, abstract theorems about Radon transforms are used to understand applied mathematics, while applied mathematics motivates some of the results in pure mathematics. Though directed at specialists in the field, the book would also be of interest to others who wish to understand current research in these areas and to witness how they relate to other branches of mathematics.

Table of Contents

  • E. D. Bolker, E. Grinberg, and J. P. S. Kung -- Admissible complexes for the combinatorial Radon transform. A Progress Report
  • Jan -- On generalized Radon transforms with unknown measures
  • W. O. Bray and D. C. Solmon -- Paley-Wiener theorems on rank one symmetric spaces of noncompact type
  • E. C. Tarabusi -- Inversion of the X-ray transform: continuous vs.discrete
  • A. M. Cormack and E. T. Quinto -- The mathematics and physics of radiation dose planning using X-rays
  • L. Ehrenpreis -- The Radon transform and tensor products
  • A. Faridani -- An application of a multidimensional sampling theorem to computed tomography
  • H. Goldschmidt -- The Radon transform for symmetric forms on real projective spaces
  • F. B. Gonzalez -- Bi-invariant differential operators on the complex motion group and the range of the \(d\)-plane transform on \(\mathbf C^n\)
  • P. R. Goodey and R. Howard -- Processes of flats induced by higher-dimensional processes II
  • A. Greenleaf and G. Uhlmann -- Microlocal techniques in integral geometry
  • S. Helgason -- The totally-geodesic Radon transform on constant curvature spaces
  • S. H. Izen -- An application for a limited solid angle X-ray transform
  • E. Lutwak -- On a conjectured projection inequality of Petty
  • P. Maass -- A generalized Radon transform in wideband radar
  • W. R. Madych -- Summability and approximate reconstruction from Radon transform data
  • F. Natterer -- An inverse problem for a transport equation and integral geometry
  • J. Orloff -- Invariant Radon transforms on a symmetric space
  • D. C. Solmon -- Nonuniqueness and the null space of the divergent beam X-ray transform
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