Overview

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.

Full Product Details

Author:   Sigurdur Helgason
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   2nd Revised edition
Volume:   v5
ISBN:  

9783764341091

ISBN 10:   3764341092
Pages:   208
Publication Date:   June 1999
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Replaced By:   9780817641092
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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; notational conventions.

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