Geodesic
A Probabilistic Approach to the Convolution Transform
Canadian mathematical bulletin, Tome 24 (1981) no. 2, pp. 205-211

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The inversion and the characterization of the convolution transform is derived via the concept of unimodality introduced by Khintchine (1938). This method yields simple and intuitively appealing proofs. 
Rivest, Louis-Paul. A Probabilistic Approach to the Convolution Transform. Canadian mathematical bulletin, Tome 24 (1981) no. 2, pp. 205-211. doi: 10.4153/CMB-1981-032-5
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