The Radon Transform
Author | : Sigurdur Helgason |
Publisher | : Springer Science & Business Media |
Total Pages | : 193 |
Release | : 2013-11-11 |
ISBN-10 | : 9781475714630 |
ISBN-13 | : 1475714637 |
Rating | : 4/5 (30 Downloads) |
Download or read book The Radon Transform written by Sigurdur Helgason and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.