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Integral Geometry and Tomography
 
Integral Geometry and Tomography
eBook ISBN:  978-0-8218-7701-2
Product Code:  CONM/113.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Integral Geometry and Tomography
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Integral Geometry and Tomography
eBook ISBN:  978-0-8218-7701-2
Product Code:  CONM/113.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 1131991; 251 pp
    MSC: Primary 00; Secondary 43; 44; 53;

    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
     
     
    • Articles
    • Ethan D. Bolker, Eric Grinberg and Joseph P. S. Kung — Admissible complexes for the combinatorial Radon transform. A progress report [ MR 1108639 ]
    • Jan Boman — On generalized Radon transforms with unknown measures [ MR 1108640 ]
    • William O. Bray and Donald C. Solmon — Paley-Wiener theorems on rank one symmetric spaces of noncompact type [ MR 1108641 ]
    • Enrico Casadio Tarabusi — Inversion of the X-ray transform: continuous vs. discrete [ MR 1108642 ]
    • A. M. Cormack and E. T. Quinto — The mathematics and physics of radiation dose planning using X-rays [ MR 1108643 ]
    • Leon Ehrenpreis — The Radon transform and tensor products [ MR 1108644 ]
    • Adel Faridani — An application of a multidimensional sampling theorem to computed tomography [ MR 1108645 ]
    • Hubert Goldschmidt — The Radon transform for symmetric forms on real projective spaces [ MR 1108646 ]
    • Fulton B. Gonzalez — Bi-invariant differential operators on the complex motion group and the range of the $d$-plane transform on ${\bf C}^n$ [ MR 1108647 ]
    • Paul R. Goodey and Ralph Howard — Processes of flats induced by higher-dimensional processes. II [ MR 1108648 ]
    • Allan Greenleaf and Gunther Uhlmann — Microlocal techniques in integral geometry [ MR 1108649 ]
    • F. Alberto Grünbaum — Backscatering comes to the rescue
    • Sigurdur Helgason — The totally-geodesic Radon transform on constant curvature spaces [ MR 1108651 ]
    • Steven H. Izen — An application for a limited solid angle X-ray transform [ MR 1108652 ]
    • Erwin Lutwak — On a conjectured projection inequality of Petty [ MR 1108653 ]
    • Peter Maass — A generalized Radon transform in wideband radar [ MR 1108654 ]
    • W. R. Madych — Summability and approximate reconstruction from Radon transform data [ MR 1108655 ]
    • Frank Natterer — An inverse problem for a transport equation and integral geometry [ MR 1108656 ]
    • Jeremy Orloff — Invariant Radon transforms on a symmetric space [ MR 1108657 ]
    • Donald C. Solmon — Nonuniqueness and the null space of the divergent beam X-ray transform [ MR 1108658 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1131991; 251 pp
MSC: Primary 00; Secondary 43; 44; 53;

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.

  • Articles
  • Ethan D. Bolker, Eric Grinberg and Joseph P. S. Kung — Admissible complexes for the combinatorial Radon transform. A progress report [ MR 1108639 ]
  • Jan Boman — On generalized Radon transforms with unknown measures [ MR 1108640 ]
  • William O. Bray and Donald C. Solmon — Paley-Wiener theorems on rank one symmetric spaces of noncompact type [ MR 1108641 ]
  • Enrico Casadio Tarabusi — Inversion of the X-ray transform: continuous vs. discrete [ MR 1108642 ]
  • A. M. Cormack and E. T. Quinto — The mathematics and physics of radiation dose planning using X-rays [ MR 1108643 ]
  • Leon Ehrenpreis — The Radon transform and tensor products [ MR 1108644 ]
  • Adel Faridani — An application of a multidimensional sampling theorem to computed tomography [ MR 1108645 ]
  • Hubert Goldschmidt — The Radon transform for symmetric forms on real projective spaces [ MR 1108646 ]
  • Fulton B. Gonzalez — Bi-invariant differential operators on the complex motion group and the range of the $d$-plane transform on ${\bf C}^n$ [ MR 1108647 ]
  • Paul R. Goodey and Ralph Howard — Processes of flats induced by higher-dimensional processes. II [ MR 1108648 ]
  • Allan Greenleaf and Gunther Uhlmann — Microlocal techniques in integral geometry [ MR 1108649 ]
  • F. Alberto Grünbaum — Backscatering comes to the rescue
  • Sigurdur Helgason — The totally-geodesic Radon transform on constant curvature spaces [ MR 1108651 ]
  • Steven H. Izen — An application for a limited solid angle X-ray transform [ MR 1108652 ]
  • Erwin Lutwak — On a conjectured projection inequality of Petty [ MR 1108653 ]
  • Peter Maass — A generalized Radon transform in wideband radar [ MR 1108654 ]
  • W. R. Madych — Summability and approximate reconstruction from Radon transform data [ MR 1108655 ]
  • Frank Natterer — An inverse problem for a transport equation and integral geometry [ MR 1108656 ]
  • Jeremy Orloff — Invariant Radon transforms on a symmetric space [ MR 1108657 ]
  • Donald C. Solmon — Nonuniqueness and the null space of the divergent beam X-ray transform [ MR 1108658 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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