Author	Helgason, Sigurdur. author
Title	The Radon Transform [electronic resource] / by Sigurdur Helgason
Imprint	Boston, MA : Springer US : Imprint: Springer, 1999
Edition	Second Edition
Connect to	http://dx.doi.org/10.1007/978-1-4757-1463-0
Descript	XIII, 193 p. online resource

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 theoยญ 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 ยง5 provides proofs of the needed results about the Riesz potentials while ยงยง3-4 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 menยญ tioned at specific places in the text. Finally I thank Jan Wetzel and Bonnie Friedman for their patient and skillful preparation of the manuscript