Logarithmic convolution
Encyclopedia
The scale convolution of two functions 
and 
, also known as their logarithmic convolution is defined as the function
when this quantity exists.
to 
:
and , also known as their logarithmic convolution is defined as the functionwhen this quantity exists.
Results
The logarithmic convolution can be related to the ordinary convolution by changing the variable from to :-
Define
and 
and let 
, then
