• A Note on the
Convolution in the Mellin Sense with Generalized Functions Adem Kilicman and Muhammad
Rezal Kamel Ariffin Abstract.
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.
