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The Radon Transform

  • Sigurdur Helgason

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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Sigurdur Helgason
    Pages 1-52
  3. Back Matter
    Pages 171-193

About this book

Introduction

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.

Keywords

group theory Lie lie group proof

Authors and affiliations

  • Sigurdur Helgason
    • 1
  1. 1.Department of MathematicsMITCambridgeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-1463-0
  • Copyright Information Springer-Verlag US 1999
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-1465-4
  • Online ISBN 978-1-4757-1463-0
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site
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