Integral Geometry and Radon Transforms
Seiten
2014
|
2011 ed.
Springer-Verlag New York Inc.
978-1-4899-9420-2 (ISBN)
Springer-Verlag New York Inc.
978-1-4899-9420-2 (ISBN)
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. From the reviews: “Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. the contents of the book is concentrated around the duality and double vibration, which is realized through the masterful treatment of a variety of examples. the book is written by an expert, who has made fundamental contributions to the area.” —Boris Rubin, Louisiana State University
Dr. Sigurdur Helgason has authored or co-authered 9 books and 94 papers. He has received numerous honors and awards, including the Steele Prize, awarded by the American Mathematical Society in 1988. He has been a professor at MIT since 1960.
The Radon Transformon Rn .- A Duality in Integral Geometry.- The Radon Transform on Two-Point Homogeneous Spaces.- The X-Ray Transform on a Symmetric Space.- Orbital Integrals.- The Mean-Value Operator.- Fourier Transforms and Distribution: A Rapid Course.- Lie Transformation Groups and Differential Operators.- Bibliography.- Notational Conventions.- Index.
| Erscheint lt. Verlag | 11.10.2014 |
|---|---|
| Zusatzinfo | 72 Illustrations, black and white; XIII, 301 p. 72 illus. |
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4899-9420-3 / 1489994203 |
| ISBN-13 | 978-1-4899-9420-2 / 9781489994202 |
| Zustand | Neuware |
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