This is a preview of subscription content, log in via an institution to check access.
Literature Cited
I. M. Gel'fand, M. I. Graev, and N. Ya. Vilenkin, Integral Geometry and Associated Problems in Theory of Representation [in Russian], Fizmatgiz, Moscow (1962).
I. M. Gel'fand, M. I. Graev, and Z. Ya. Shapiro, "Integral geometry on k-dimensional planes," Funkts. Anal. Prilozhen.,1, No. 1, 15–31 (1967).
I. M. Gel'fand and M. I. Graev, "Complexes of k-dimensional planes and the Plancherel formula for SL (n; C)," Dokl. Akad. Nauk SSSR,179, No. 3, 522–525 (1968).
I. M. Gel'fand and M. I. Graev, "Admissible complexes of lines in Cn," Funkts. Anal. Prilozhen.,2, No. 3, 39–52 (1968).
K. Maius, "Admissible complexes with one critical point," Funkts. Anal. Prilozhen.,9, No. 2, 81–82 (1975).
I. M. Gel'fand and S. G. Gindikin, "Nonlocal inversion formulas in real integral geometry," Funkts. Anal. Prilozhen.,11, No. 3, 12–19 (1979).
S. Helgason, "Differential operators on homogeneous spaces," Acta Math.,102, 239–299 (1959).
S. Helgason, "Duality and Radon transform for symmetric spaces," Am. J. Math.85, 667–692 (1963).
I. M. Gel'fand and M. I. Graev, "Geometry of homogeneous spaces, representations of groups in homogeneous spaces, and associated problems of integral geometry. I," Tr. Mosk. Mat. Ob-va,8, 321–390 (1959).
S. G. Gindikin and F. I. Karpelevich, "On a problem in integral geometry," in: In Memory of N. G. Chebotarev [in Russian], Kazan. Univ. (1964), pp. 30–43.
V. I. Arnol'd, Supplementary Chapters to the Theory of Ordinary Differential Equations [in Russian], Nauka, Moscow (1978).
E. Cartan, "Sur les variétés à connection projective," Bull. Soc. Math. France,52, 205–241 (1924); Oeuvres, III,1, No. 70, Paris, 825–862 (1955).
R. G. Mukhometov, "On a problem of integral geometry," in: Mathematical Problems of Geophysics [in Russian], No. 6, Part 2, Computing Center of the Academy of Sciences of the USSR, Siberian Branch (1975), pp. 212–242.
V. G. Romanov, "Integral geometry on the geodesics of an isotropic Riemannian metric," Dokl. Akad. Nauk SSSR,241, No. 2, 290–293 (1978).
I. N. Bernshteian and M. L. Gerver, "On a problem of integral geometry for a family of geodesics and the converse kinematic problem of seismics," Dokl. Akad. Nauk SSSR,243, No. 2, 302–305 (1978).
V. Guillemin and S. Shternberg, Geometric Asymptotics, Am. Math. Soc., Providence, R. I. (1977).
I. M. Gel'fand, M. I. Graev, and Z. Ya. Shapiro, "Integral geometry in projective space," Funkts. Anal. Prilozhen.,4, No. 1, 14–32 (1970).
Additional information
Institute of Applied Mathematics, Academy of Sciences of the USSR, Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 13, No. 2, pp. 11–31, April–June, 1979.
Rights and permissions
About this article
Cite this article
Gel'fand, I.M., Gindikin, S.G. & Shapiro, Z.Y. A local problem of integral geometry in a space of curves. Funct Anal Its Appl 13, 87–102 (1979). https://doi.org/10.1007/BF01077241
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01077241