Geodesic
On inversion of the convolution transform
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (1985), pp. 3-12 Cet article a éte moissonné depuis la source Math-Net.Ru

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In all works known in the literature devoted to the inversion of a convolution-type transformation, the same approach is used, based on the fundamental works of Widder and Hirschman. In the article we propose a different approach, reducing this transformation to the Laplace transform of another function, from which the inversion is then obtained. 
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G. V. Badalyan; V. M. Edigarian. On inversion of the convolution transform. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (1985), pp. 3-12. http://geodesic.mathdoc.fr/item/UZERU_1985_1_a0/

[1] I. I. Khirshman, D. V. Uidder, Preobrazovaniya tipa svertki, IL, M., 1958

[2] G. V. Badalyan, “Primenenie preobrazovaniya tipa svertki k teorii obobschennoi problemy momentov Stiltesa”, IAN SSSR, ser. Mat., 1967, no. 31, 491–530

[3] G. V. Badalyan, “O klassifikatsii i predstavlenii beskonechno differentsiruemykh funktsii”, IAN SSSR, ser. Mat., 1970, no. 34, 584–620 | Zbl

[4] Y. Tanno, “On the convolution transform”, Kodai Math. Sem. rep., 1959, no. 2, 40–50 | MR | Zbl

[5] Y. Tanno, “On a class of convolution transforms”, Tohoku Math. J., 18:2 (1966), 156–173 | DOI | MR | Zbl

[6] Z. Ditzian, A Jakimovski, “Properties of Kernels for a class of convolution transforms”, Tohoku Math. J., 20:2 (1968), 175–198 | MR | Zbl

[7] G. V. Badalyan, “Uslovie razlozhimosti funktsii v obobschennyi stepennoi ryad vne osnovnogo promezhutka”, IAN SSSR, ser. Mat., 1962, no. 26, 313–328 | Zbl

[8] E. Titchmarsh, Vvedenie v teoriyu integrala Fure, Gostekhizdat, M.-L., 1948