Skip to main content
Log in

A problem of integral geometry and a linearized inverse problem for a hyperbolic equation

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. I. M. Gel'fand, M. I. Graev, and N. Ya. Vilenkin, Generalized Functions. Integral Geometry and Representation Theory [in Russian], Fizmatgiz, Moscow (1962).

    Google Scholar 

  2. F. John, Plane Waves and Spherical Means, Applied to Partial Differential Equations, Wiley (Interscience), New York (1955).

    Google Scholar 

  3. R. Courent, Partial Differential Equations [Russian translation], Izd. Mir, Moscow (1964).

    Google Scholar 

  4. 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).

    Google Scholar 

  5. M. M. Lavrent'ev and Vasil'ev, Multidimensional Inverse Problems for Differential Equations [in Russian], Nauka, Novosibirsk (1968).

    Google Scholar 

  6. 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).

    Google Scholar 

  7. 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).

    Google Scholar 

  8. G. Muntz, Integral Equations [Russian translation], Vol. 1, GTTI, Moscow-Leningrad (1934).

    Google Scholar 

  9. S. L. Sobolev, “The wave equation for a nonhomogeneous medium,” Trudy Seism. In-ta, No. 6, 1–57 (1930).

    Google Scholar 

  10. 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).

    Google Scholar 

Download references

Authors

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 10, No. 6, pp. 1364–1374, November–December, 1969.

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00990776

Keywords

Navigation