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A duality in integral geometry; some generalizations of the Radon transform
Author:
Sigurdur Helgason
Journal:
Bull. Amer. Math. Soc. 70 (1964), 435-446
MathSciNet review:
0166795
Full-text PDF
References |
Additional Information
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- W. A. Borovikov, Fundamental solutions of linear partial differential equations with constant coefficients, Trudy Moscov. Mat. Obšč. 8 (1959), 199-257. MR 123087
- 2.
- R. Courant and A. Lax, Remarks on Cauchy's problem for hyperbolic partial differential equations with constant coefficients in several independent variables, Comm. Pure Appl. Math. 8 (1955), 497-502. MR 75430
- 3.
- P. Funk, Über eine geometrische Anwendung der Abelschen Integralgleichung, Math. Ann. 77 (1916), 129-135. MR 1511851
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- L. Gårding, Transformation de Fourier des distributions homogènes, Bull. Soc. Math. France 89 (1961), 381-428. MR 149195
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- 6.
- I. M. Gelfand and M. I. Graev, Analogue of the Plancherel formula for the classical groups, Trudy Moscov. Mat. Obšč. 4 (1955), 375-404. MR 71714
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- I. M. Gelfand and M. I. Graev, The geometry of homogeneous spaces, group representations in homogeneous spaces and questions in integral geometry related to them. I, Trudy Moscov. Mat. Obšč. 8(1959), 321-390.
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- I. M. Gelfand, M. I. Graev and N. Vilenkin, Integral geometry and its relation to problems in the theory of group representations, Vol. 5, Generalized Functions, Fizmatgiz, Moscow, 1962.
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- I. M. Gelfand and S. J. Shapiro, Homogeneous functions and their applications, Uspehi Mat. Nauk 10 (1955), 3-70. MR 73042
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- 12.
- Harish-Chandra, The Plancherel formula for complex semisimple Lie groups, Trans. Amer. Math. Soc. 76 (1954), 485-528. MR 63376
- 13.
- Harish-Chandra, Fourier transforms on a semisimple Lie algebra. I, II, Amer. J. Math. 79 (1957), 193-257; 653-686. MR 87044
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- S. Helgason, Differential operators on homogeneous spaces, Acta Math. 102 (1959), 239-299. MR 117681
- 17.
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- S. Helgason, Fundamental solutions of invariant differential operators on symmetric spaces, Bull. Amer. Math. Soc. 69 (1963), 778-781. MR 156919
- 21.
- S. Helgason, The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds(to appear). MR 172311
- 22.
- S. Helgason, The Plancherel formula for the Radon transform on symmetric spaces(to appear).
- 23.
- F. John, Bestimmung einer Funktion aus ihren Integralen über gewisse Mannigfaltigkeiten, Math. Ann. 100 (1934), 488-520. MR 1512906
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9904-1964-11147-2
PII:
S 0002-9904(1964)11147-2
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