Geodesic
On convolution transforms whose inversion functions have complex roots
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2003), pp. 3-7.

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For convolution transforms it has been received inversion formula, when $\phi(x)=L^{2}(-\infty, +\infty)$, and inversion functions $E(s)=\prod\limits_{k=1}^{\infty}\Big(1-\dfrac{s^2}{a_k^2} \Big)$ have complex roots satisfying to conditions $$\sum\limits_{k=1}^{\infty}+\infty \dfrac {1}{|a _k|^2},~~|\arg a_k| \le \dfrac{\pi}{4}.$$
Keywords: Convolution transforms, complex roots. 
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S. A. Akopyan. On convolution transforms whose inversion functions have complex roots. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2003), pp. 3-7. http://geodesic.mathdoc.fr/item/UZERU_2003_3_a0/

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