Literature Cited
I. M. Gel'fand, M. I. Graev, and N. Ya. Vilenkin, Generalized Functions. Integral Geometry and Representation Theory [in Russian], Fizmatgiz, Moscow (1962).
F. John, Plane Waves and Spherical Means, Applied to Partial Differential Equations, Wiley (Interscience), New York (1955).
R. Courent, Partial Differential Equations [Russian translation], Izd. Mir, Moscow (1964).
M. M. Lavrent'ev and V. G. Romanov, “On three linearized inverse problems for hyperbolic equations,” Dokl. Akad. Nauk SSSR,171, No. 6, 1279–1281 (1966).
M. M. Lavrent'ev and Vasil'ev, Multidimensional Inverse Problems for Differential Equations [in Russian], Nauka, Novosibirsk (1968).
V. G. Romanov, “On the reconstruction of a function from integrals over ellipsoids of rotation for which one focus is fixed,” Dokl. Akad. Nauk SSSR,173, No. 4, 766–769 (1967).
V. G. Romanov, “On the reconstruction of a function from integrals over a family of curves,” Sib. matem. Zh.,8, No. 5, 1206–1208 (1967).
G. Muntz, Integral Equations [Russian translation], Vol. 1, GTTI, Moscow-Leningrad (1934).
S. L. Sobolev, “The wave equation for a nonhomogeneous medium,” Trudy Seism. In-ta, No. 6, 1–57 (1930).
S. L. Sobolev, “On a problem concerning the integration of the wave equation in a nonhomogeneous medium,” Trudy Seism. In-ta, No. 42, 1–26 (1934).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 10, No. 6, pp. 1364–1374, November–December, 1969.
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Romanov, V.G. A problem of integral geometry and a linearized inverse problem for a hyperbolic equation. Sib Math J 10, 1011–1018 (1969). https://doi.org/10.1007/BF00990776
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DOI: https://doi.org/10.1007/BF00990776