Integral Geometry and Radon Transforms

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Sigurdur Helgason - Integral Geometry and Radon Transforms
Published: 2010-11-17 | ISBN: 1441960546 | PDF | 316 pages | 3 MB

In this text, integral geometry deals with Radon's problem of representing a function on a manifold in terms of its integrals over certain submanifolds-hence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial di erential equations and group representations). For the case of the plane, the inversion theorem and the support theorem have had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroom use or self-study. A number of exercises point to further results with documentation.
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Tags: Transforms, Geometry, Integral
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