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Selected topics in integral geometry

Author: I M Gelʹfand; S G Gindikin; M I Graev
Publisher: Providence, R.I. : American Mathematical Society, ©2003.
Series: Translations of mathematical monographs, v. 220.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Gelʹfand, I.M. (Izrailʹ Moiseevich).
Selected topics in integral geometry.
Providence, R.I. : American Mathematical Society, ©2003
(DLC) 2003052222
(OCoLC)52288750
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: I M Gelʹfand; S G Gindikin; M I Graev
ISBN: 9781470446444 1470446448
OCLC Number: 1031956820
Description: 1 online resource
Contents: Radon 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
Series Title: Translations of mathematical monographs, v. 220.
Other Titles: Izbrannye zadachi integralʹnoĭ geometrii.
Responsibility: I.M. Gelfand, S.G. Gindikin, M.I. Graev ; [translated from the Russian by A. Shtern].

Abstract:

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 d.

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