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The Radon Transform
Abstract
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.
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Metadata
- Authors
- Helgason, S.
- Venue
- Progress in Mathematics
- Publisher
- Springer US
- Published
- 1999
- ISSN
- 0743-1643 (ISSN-L)
- 2296-505X
- OpenAlex
- W1586402789
- Cited by
- 1,166
- References
- 0
- FWCI
- 6.07
- Type
- book
- Language
- en
- Open access
- closed
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