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Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.:

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Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 1980, Volume 16, Pages 53–226 (Mi intd46)  

This article is cited in 19 scientific papers (total in 21 papers)

Integral geometry in affine and projective spaces

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

Abstract: A survey is given of results of integral geometry related to the integration of sections of one-dimensional bundles and differential forms over planes in affine and projective spaces.

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English version:
Journal of Soviet Mathematics, 1982, 18:1, 39–167

Bibliographic databases:

UDC: 517.986.64

Citation: I. M. Gel'fand, S. G. Gindikin, M. I. Graev, “Integral geometry in affine and projective spaces”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 16, VINITI, Moscow, 1980, 53–226; J. Soviet Math., 18:1 (1982), 39–167

Citation in format AMSBIB
\by I.~M.~Gel'fand, S.~G.~Gindikin, M.~I.~Graev
\paper Integral geometry in affine and projective spaces
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat.
\yr 1980
\vol 16
\pages 53--226
\publ VINITI
\publaddr Moscow
\jour J. Soviet Math.
\yr 1982
\vol 18
\issue 1
\pages 39--167

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    This publication is cited in the following articles:
    1. A. B. Goncharov, “Infinitesimal structures related to Hermitian symmetric spaces”, Funct. Anal. Appl., 15:3 (1981), 221–223  mathnet  crossref  mathscinet  zmath  isi
    2. I. M. Gel'fand, M. I. Graev, R. Roshu, “Nonlocal inversion formulas in a problem of integral geometry related to $p$-dimensional planes in real projective space”, Funct. Anal. Appl., 16:3 (1982), 196–198  mathnet  crossref  mathscinet  zmath  isi
    3. K. Maius, “Integral geometry on linear complexes of lines”, Funct. Anal. Appl., 16:3 (1982), 221–223  mathnet  crossref  mathscinet  zmath  isi
    4. N. N. Bogolyubov, S. G. Gindikin, A. A. Kirillov, A. N. Kolmogorov, S. P. Novikov, L. D. Faddeev, “Izrail' Moiseevich Gel'fand (on his seventieth birthday)”, Russian Math. Surveys, 38:6 (1983), 145–153  mathnet  crossref  mathscinet  zmath  adsnasa
    5. S. G. Gindikin, “Integral formulas and integral geometry for $\bar\partial$-cohomologies in $\mathbb{CP}^n$”, Funct. Anal. Appl., 18:2 (1984), 108–119  mathnet  crossref  mathscinet  zmath  isi
    6. P. L. Polyakov, G. M. Henkin, “Homotopy formulas for the $\overline\partial$-operator on $\mathbf CP^n$ and the Radon–Penrose transform”, Math. USSR-Izv., 28:3 (1987), 555–587  mathnet  crossref  mathscinet  zmath
    7. I. M. Gel'fand, A. V. Zelevinskii, “Algebraic and combinatorial aspects of the general theory of hypergeometric functions”, Funct. Anal. Appl., 20:3 (1986), 183–197  mathnet  crossref  mathscinet  zmath  isi
    8. I. M. Gel'fand, V. V. Minakhin, V. N. Shander, “Integration on supermanifolds and Radon supertransformations”, Funct. Anal. Appl., 20:4 (1986), 310–312  mathnet  crossref  mathscinet  zmath
    9. A. V. Zorich, “Integration of pseudodifferential forms and inversion of Radon-type integral transformations”, Russian Math. Surveys, 42:4 (1987), 151–152  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    10. A. N. Varchenko, “Combinatorics and topology of the disposition of affine hyperplanes in real space”, Funct. Anal. Appl., 21:1 (1988), 9–19  mathnet  crossref  mathscinet  zmath  isi
    11. B. Yu. Sternin, V. E. Shatalov, “Differential equations on complex-analytic manifolds, and the Maslov canonical operator”, Russian Math. Surveys, 43:3 (1988), 117–148  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    12. A. B. Goncharov, “Integral geometry on families of k-dimensional submanifolds”, Funct. Anal. Appl., 23:3 (1989), 178–189  mathnet  crossref  mathscinet  zmath  isi
    13. I. M. Gel'fand, M. I. Graev, V. S. Retakh, “General hypergeometric systems of equations and series of hypergeometric type”, Russian Math. Surveys, 47:4 (1992), 1–88  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    14. F. F. Voronov, “A complex generated by variational derivatives. A Lagrange formalism of infinite order and a generalization of Stokes's theorem”, Russian Math. Surveys, 51:6 (1996), 1229–1230  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    15. M. I. Graev, “Integral Geometry on the Space $L^n$, where $L$ is a Matrix Ring”, Funct. Anal. Appl., 30:4 (1996), 277–280  mathnet  crossref  crossref  mathscinet  zmath  isi
    16. I. M. Gel'fand, M. I. Graev, “$GG$-functions and their relation to general hypergeometric functions”, Russian Math. Surveys, 52:4 (1997), 639–684  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    17. E. E. Petrov, “Paley–Wiener theorems for the matrix Radon transform”, Sb. Math., 190:8 (1999), 1173–1193  mathnet  crossref  crossref  mathscinet  zmath  isi
    18. M. I. Graev, “A Problem of Integral Geometry Related to a Triple of Grassmann Manifolds”, Funct. Anal. Appl., 34:4 (2000), 299–301  mathnet  crossref  crossref  mathscinet  zmath  isi
    19. M. I. Graev, “Relatively Closed Operators Associated to a Pair of Grassmannians”, Math. Notes, 71:1 (2002), 56–67  mathnet  crossref  crossref  mathscinet  zmath  isi
    20. A. B. Sekerin, “Applications of the Radon transform in the theory of plurisubharmonic functions”, Russian Math. (Iz. VUZ), 47:2 (2003), 44–52  mathnet  mathscinet  zmath  elib
    21. A. M. Vershik, I. M. Gel'fand, S. G. Gindikin, A. A. Kirillov, G. L. Litvinov, V. F. Molchanov, Yu. A. Neretin, V. S. Retakh, “Mark Iosifovich Graev (to his 85th brithday)”, Russian Math. Surveys, 63:1 (2008), 173–188  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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