Helgason S. Radon Transform

2nd ed. — Birkhäuser, 1999. — 197 p.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 of the explicit inversion formulas and range theorems 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 V on 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 Hӧrmander'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.The Radon Transform on Rⁿ
A Duality in Integral Geometry
The Radon Transform on Two-point Homogeneous Spaces
Orbital Integrals
Fourier Transforms and Distributions. A Rapid Course