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OverviewThe miracle of integral geometry is that it is often possible to recover a function on a manifold just from the knowledge of its integrals over certain submanifolds. The founding example is the Radon transform, introduced at the beginning of the 20th century. Since then, many other transforms were found, and the general theory was developed. Moreover, many important practical applications were discovered. The best known, but by no means the only one, being to medical tomography. This book is a general introduction to integral geometry, the first from this point of view for almost four decades. The authors, all leading experts in the field, represent one of the most influential schools in integral geometry. The book presents in detail basic examples of integral geometry problems, such as the Radon transform on the plane and in space, the John transform, the Minkowski-Funk transform, integral geometry on the hyperbolic plane and in the hyperbolic space, the horospherical transform and its relation to representations of $SL(2,\mathbb C)$, integral geometry on quadrics, etc. The study of these examples allows the authors to explain important general topics of integral geometry, such as the Cavalieri conditions, local and nonlocal inversion formulas, and overdetermined problems in integral geometry. Many of the results in the book were obtained by the authors in the course of their career-long work in integral geometry. This book is suitable for graduate students and researchers working in integral geometry and its applications. Full Product DetailsAuthor: I. M. Gelfand , Simon Gindikin , M. I. GraevPublisher: American Mathematical Society Imprint: American Mathematical Society Edition: illustrated edition Volume: No. 220 Dimensions: Width: 17.10cm , Height: 1.30cm , Length: 26.00cm Weight: 0.533kg ISBN: 9780821829325ISBN 10: 0821829327 Pages: 170 Publication Date: 30 September 2003 Audience: General/trade , College/higher education , General , Tertiary & Higher Education Format: Hardback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsRadon transform John transform Integral geometry and harmonic analysis on the hyperbolic plane and in the hyperbolic space Integral geometry and harmonic analysis on the group ${G=SL(2,\mathbb C)}$ Integral geometry on quadrics Bibliography Index.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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