Geodesic
On some classes of uniqueness for the solution of integral geometry problems
Matematičeskie zametki, Tome 16 (1974) no. 4, pp. 657-668 
V. G. Romanov. On some classes of uniqueness for the solution of integral geometry problems. Matematičeskie zametki, Tome 16 (1974) no. 4, pp. 657-668. http://geodesic.mathdoc.fr/item/MZM_1974_16_4_a18/
@article{MZM_1974_16_4_a18,
     author = {V. G. Romanov},
     title = {On some classes of uniqueness for the solution of integral geometry problems},
     journal = {Matemati\v{c}eskie zametki},
     pages = {657--668},
     year = {1974},
     volume = {16},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_4_a18/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.