The Radon Transform [Hardcover]

The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications, namely to partial differential equations, group representations, X-ray technology, nuclear magnetic resonance scanning, and tomography. This second edition, significantly expanded and updated, presents new material taking into account some of the progress made in the field since 1980. Aimed at beginning graduate students, this monograph will be useful in the classroom or as a resource for self-study. Readers will find here an accessible introduction to Radon transform theory, an elegant topic in integral geometry.

Preface to the Second Edition.-Preface to the First Edition.-The Radon Transform on Rⁿ.-A Duality in Integral Geometry. Generalized Radon Transforms and Orbital Integrals.-The Radon Transform on Two-Point Homogeneous Spaces.-Orbital Integrals and the Wave Operator for Isotropic Lorentz Spaces.-Fourier Transforms and Distributions. A Rapid Course.-Bibliography.-Notational Conventions.-Subject Index.

This is the second edition of the famous book by Sigurdur Helgason which has been updated in accordance with recent new results in this area. The list of references and bibliographical notes have been essentially extended. Many examples with explicit inversion formulas and range theorems have been added, and the group-theoretic viewpoint is emphasized... [the] author adds a new chapter, Chapter 5, which contains useful information about Fourier transforms, distributions and Riesz potentials. The second edition preserves the nice introductory flavor of the first one. The book will be highly appreciated by the mathematical community.

--Mathematical Reviews (on the second edition)

l£¾