Definition
The scale convolution of two functions and , also known as their logarithmic convolution is defined as the function
1 1
when this quantity exists.
Results
The logarithmic convolution can be related to the ordinary convolution by changing the variable from to :
1
Define and and let , then
s \ast_l r(v) = f \ast g(v) = g \ast f(v) = r \ast_l s(v).