Logarithmic convolution

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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).

logarithmic convolution at PlanetMath.