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The Radon Transform

  • Book
  • © 1999

Overview

Authors:
  1. Sigurdur Helgason

    1. Department of Mathematics, MIT, Cambridge, USA

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Part of the book series: Progress in Mathematics (PM, volume 5)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xiii
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  2. The Radon Transform on ℝn

    • Sigurdur Helgason
    Pages 1-52

  3. A Duality in Integral Geometry. Generalized Radon Transforms and Orbital Integrals

    • Sigurdur Helgason
    Pages 53-81

  4. The Radon Transform on Two-Point Homogeneous Spaces

    • Sigurdur Helgason
    Pages 83-122

  5. Orbital Integrals and the Wave Operator for Isotropic Lorentz Spaces

    • Sigurdur Helgason
    Pages 123-146

  6. Fourier Transforms and Distributions. A Rapid Course

    • Sigurdur Helgason
    Pages 147-169

  7. Back Matter

    Pages 171-193
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Keywords

About this book

The first edition of this book has been out of print for some time and I have decided to follow the publisher's kind suggestion to prepare a new edition. Many examples with explicit inversion formulas and range theo­ rems have been added, and the group-theoretic viewpoint emphasized. For example, the integral geometric viewpoint of the Poisson integral for the disk leads to interesting analogies with the X-ray transform in Euclidean 3-space. To preserve the introductory flavor of the book the short and self-contained Chapter Von Schwartz' distributions has been added. Here §5 provides proofs of the needed results about the Riesz potentials while §§3-4 develop the tools from Fourier analysis following closely the account in Hormander's books (1963] and [1983]. There is some overlap with my books (1984] and [1994b] which however rely heavily on Lie group theory. The present book is much more elementary. I am indebted to Sine Jensen for a critical reading of parts of the manuscript and to Hilgert and Schlichtkrull for concrete contributions men­ tioned at specific places in the text. Finally I thank Jan Wetzel and Bonnie Friedman for their patient and skillful preparation of the manuscript.

Authors and Affiliations

  • Department of Mathematics, MIT, Cambridge, USA

    Sigurdur Helgason

Bibliographic Information

  • Book Title: The Radon Transform

  • Authors: Sigurdur Helgason

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-1463-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Sigurdur Helgason 1999

  • Softcover ISBN: 978-1-4757-1465-4Published: 09 October 2013

  • eBook ISBN: 978-1-4757-1463-0Published: 11 November 2013

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: XIII, 193

  • Number of Illustrations: 9 b/w illustrations

  • Topics: Algebra, Mathematics, general

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