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© 1999

The Radon Transform

Book

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

  1. 1.Department of MathematicsMITCambridgeUSA

Bibliographic information

  • Book Title The Radon Transform
  • Authors Sigurdur Helgason
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • 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
  • Hardcover ISBN 978-0-306-39205-4
  • Softcover ISBN 978-1-4757-1465-4
  • eBook ISBN 978-1-4757-1463-0
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 1
  • Number of Pages XIII, 193
  • Number of Illustrations 9 b/w illustrations, 0 illustrations in colour
  • Topics Algebra
    Mathematics, general
  • Buy this book on publisher's site