The Radon Transform

1. Front Matter

   Pages i-xiii

   PDF

2. The Radon Transform on ℝn

   • Sigurdur Helgason

   Pages 1-52

3. A Duality in Integral Geometry. Generalized Radon Transforms and Orbital Integrals

   • Sigurdur Helgason

   Pages 53-81

4. The Radon Transform on Two-Point Homogeneous Spaces

   • Sigurdur Helgason

   Pages 83-122

5. Orbital Integrals and the Wave Operator for Isotropic Lorentz Spaces

   • Sigurdur Helgason

   Pages 123-146

6. Fourier Transforms and Distributions. A Rapid Course

   • Sigurdur Helgason

   Pages 147-169

7. Back Matter

   Pages 171-193

   PDF

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.

• group theory
• Lie
• lie group
• proof

• Department of Mathematics, MIT, Cambridge, USA

  Sigurdur Helgason

Policies and ethics