Selected Topics in Integral Geometry by I. M. Gel'fand, M. I. Graev, S. G. Gindikin | | 9780821829325 | Hardcover | Barnes & Noble
Selected Topics in Integral Geometry

Selected Topics in Integral Geometry

by I. M. Gel'fand, M. I. Graev, S. G. Gindikin
     
 

ISBN-10: 0821829327

ISBN-13: 9780821829325

Pub. Date: 09/02/2003

Publisher: American Mathematical Society

The 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

Overview

The 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. The present 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. Many of the results in the book were obtained by the authors in the course of their career-long work in integral geometry.

Product Details

ISBN-13:
9780821829325
Publisher:
American Mathematical Society
Publication date:
09/02/2003
Series:
Translations of Mathematical Monographs, #220
Pages:
170
Product dimensions:
7.20(w) x 10.20(h) x 0.60(d)

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