Geodesic
A Note on the Convolution in the Mellin Sense with Generalized Functions
Bulletin of the Malaysian Mathematical Society, Tome 25 (2002) no. 2 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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The classical convolution is given by the following equation and is widely accessible in many literatures including its extension to generalized functions (Gelfand and Shilov [4], A. Zemanian [2]). Another form of convolution is given by the Mellin convolution (i.e. convolution in the Mellin sense) which is given by The theory of the convolution in the Mellin sense for Mellin transformable functions is well known (Butzer and Jansche [3], Srivastava and Buschman [6]). In this work we extend this setting to the generalized functions. 
@article{BMMS_2002_25_2_a0,
     author = {Adem Kilicman and Muhammad Rezal Kamel Ariffin},
     title = {A {Note} on the
                          {Convolution} in the {Mellin} {Sense} with {Generalized} {Functions}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2002},
     volume = {25},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2002_25_2_a0/}
}
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                          Convolution in the Mellin Sense with Generalized Functions
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Adem Kilicman; Muhammad Rezal Kamel Ariffin. A Note on the
                          Convolution in the Mellin Sense with Generalized Functions. Bulletin of the Malaysian Mathematical Society, Tome 25 (2002) no. 2. http://geodesic.mathdoc.fr/item/BMMS_2002_25_2_a0/