Geodesic
On inversion of the convolution transform
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (1985), pp. 3-12

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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/