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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:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

Presents 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  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: I M Gelʹfand; S G Gindikin; M I Graev
ISBN: 0821829327 9780821829325
OCLC Number: 52288750
Description: ix, 170 pages : illustrations ; 26 cm.
Contents: Ch. 1. Radon Transform --
1. Radon transform on the plane --
2. Radon transform in three-dimensional space --
3. Wave equation and the Huygens principle --
4. Cavalieri's conditions and Paley-Wiener theorems for the Radon transform --
5. Poisson formula for the Radon transform, and the discrete Radon transform --
6. Minkowski-Funk transform --
7. Radon transform of differential forms --
8. Radon transform for the projective plane and projective space --
9. Radon transform on the complex affine space --
Ch. 2. John Transform --
1. John transform in the real affine space --
2. John transform of differential forms on R[superscript 3] --
3. John transform in the three-dimensional real projective space --
4. John transform in the complex affine space --
5. Problems of integral geometry for line complexes in C[superscript 3] --
Ch. 3. Integral Geometry and Harmonic Analysis on the Hyberbolic Plane and in the Hyperbolic Space --
1. Elements of hyperbolic planimetry --
2. Horocycle transform --
3. Analog of the Fourier transform on the hyperbolic plane and the relation between this analog and the horocycle transform --
4. Relation to the representation theory of the group SL(2,R) --
5. Integral transform related to lines (geodesics) on the hyperbolic plane L[superscript 2] --
6. Horospherical transform in the three-dimensional hyperbolic space L[superscript 3] --
7. Analog of the Fourier transform in the hyperbolic space, and its relation to the horospherical transform --
8. Relation to the representation theory for the group SL(2,C) --
9. Wave equation for the hyperbolic plane and hyperbolic space, and the Huygens principle --
Ch. 4. Integral Geometry and Harmonic Analysis on the Group G = SL(2,C) --
1. Geometry on the group G --
2. Integral geometry on the group G = SL(2,C) --
3. Harmonic analysis on the group G = SL(2,C) --
4. Another version of the Fourier transform on G = SL(2,C) --
Ch. 5. Integral Geometry on Quadrics. 1. Integral transform related to the hyperplane sections of a hyperboloid of two sheets in R[superscript n+1] --
2. Integral transform related to spheres in Euclidean space E[superscript n].
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].

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