The Radon Transform

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.

Product details

• Authors: Sigurdur Helgason
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 22.04.2014
• EAN: 9781475714654
• ISBN: 978-1-4757-1465-4
• No. of pages: 193
• Dimensions: 162 mm x 12 mm x 231 mm
• Weight: 311 g
• Illustrations: XIII, 193 p. 9 illus.
• Series: Progress in Mathematics; Progress in Mathematics
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra