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On some classes of uniqueness for the solution of integral geometry problems

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Abstract

We consider the problem of determining a function from a knowledge of integrals of the function along families of curves with a known weight function. For sufficiently general assumptions on the family of curves and on the weight function the problem is reduced to the solution of an integrodifferential equation. We establish the uniqueness of the solution of this equation in certain classes of functions.

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Literature cited

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Authors and Affiliations

  1. Computer Center, Siberian Branch, Academy of Sciences of the USSR, USSR

    V. G. Romanov

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  1. V. G. Romanov
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Additional information

Translated from Matematicheskie Zametki, Vol. 16, No. 4, pp. 657–668, October, 1974.

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Romanov, V.G. On some classes of uniqueness for the solution of integral geometry problems. Mathematical Notes of the Academy of Sciences of the USSR 16, 983–989 (1974). https://doi.org/10.1007/BF01104268

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  • DOI: https://doi.org/10.1007/BF01104268

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