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Explicit inversion formulas for the ray transform in spaces of constant curvature

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References

  1. V. P. Palamodov, Selected Topics in Integral Geometry. Pure and Applied, Lecture for F. Klein Colloquium, Düsseldorf Universität, Düsseldorf (1994).

  2. V. P. Palamodov, “Reconstruction from line integrals in spaces of constant curvature,” Math. Nachr. (to appear.)

  3. S. Helgason, Geometric Analysis on Symmetric Spaces, Amer. Math. Soc., Providence (1994). (Math. Surveys and Monographs;39.)

    MATH  Google Scholar 

  4. F. Natterer, The Mathematics of Computerized Tomography [Russian translation], Mir, Moscow (1990).

    MATH  Google Scholar 

  5. I. M. Gel'fand and M. I. Graev, “Line complexes in the spaceC n”, Funktsional. Anal. i Prilozhen.,2, No. 3, 39–52 (1968).

    MathSciNet  Google Scholar 

  6. V. P. Palamodov, “Inversion formulas for the three-dimensional ray transform,” Lecture Notes in Math.,1497, 53–62 (1990).

    Article  MathSciNet  Google Scholar 

  7. V. P. Palamodov, “Radon transform on real algebraic varieties,” in: 75 Years of Radon Transform (Vienna, 1992), International Press, Cambridge, 1994, pp. 252–262.

    Google Scholar 

  8. A. S. Denisjuk, “Inversion of the generalized Radon transform,” Amer. Math. Soc. Transl. Ser. 2,162, 19–32 (1994).

    Google Scholar 

  9. A. S. Denisjuk, “On exact explicit formulae for inversion ofX-ray transform,” in: Proceedings of the International Symposium on Computerized Tomography, Novosibirsk, 1995.

  10. J. A. Wolf, Spaces of Constant Curvature [Russian translation], Nauka, Moscow (1982).

    MATH  Google Scholar 

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The research was financially supported by the International Science Foundation (Grant N2E000).

Brest. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 38, No. 5, pp. 1058–1070, September–October, 1997.

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Denisyuk, A.S. Explicit inversion formulas for the ray transform in spaces of constant curvature. Sib Math J 38, 915–925 (1997). https://doi.org/10.1007/BF02673033

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  • DOI: https://doi.org/10.1007/BF02673033

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