| Description |
1 online resource (viii, 400 pages) : illustrations. |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
Encyclopedia of mathematics and its applications ; volume 106
|
|
Encyclopedia of mathematics and its applications ; volume 106.
|
| Bibliography |
Includes bibliographical references (pages 363-391) and indexes. |
| Contents |
Introduction -- Computerized tomography, x-rays, and the radon transform -- Radon transform -- The k-plane transform, Radon-John transform -- Range and differential equations -- Generalizations and variants of the radon transform |
| Summary |
This book is a comprehensive study of the Radon transform, which operates on a function by integrating it over hyperplanes. The book begins with an elementary and graphical introduction to the Radon transform, tomography and CT scanners, followed by a rigorous development of the basic properties of the Radon transform. Next the author introduces Grassmann manifolds in the study of the k-plane transform (a version of the Radon transform) which integrates over k-dimensional planes rather than hyperplanes. The remaining chapters are concerned with more advanced topics, such as the attenuated Radon transform and generalized Radon transforms defined by duality of homogeneous spaces and double fibrations. Questions of invertibility and the range of the Radon transform are dealt with and inversion formulas are developed with particular attention to functions on L2 spaces and some discussion of the case of Lp spaces. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Radon transforms.
|
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Radon transforms. |
|
Geometric tomography.
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Geometric tomography. |
| Genre/Form |
Electronic books.
|
|
Electronic book.
|
| Other Form: |
Print version: Markoe, Andrew, 1943- Analytic tomography 0521793475 (DLC) 2005022524 (OCoLC)61204425 |
| ISBN |
9781461941477 (electronic book) |
|
1461941474 (electronic book) |
|
9780511530012 (ebook) |
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0511530013 (ebook) |
|
0521793475 |
|
9780521793476 |
|
