logarithmic convolution


The scale convolution of two functions s(t) and r(t), also known as their logarithmic convolution is defined as the function


when this quantity exists.


The logarithmic convolution can be related to the ordinary convolution by changing the variable from t to v=logt:

slr(t) = 0s(ta)r(a)daa=-s(teu)r(eu)𝑑u
= -s(elogt-u)r(eu)𝑑u

Define f(v)=s(ev) and g(v)=r(ev) and let v=logt, then

Title logarithmic convolution
Canonical name LogarithmicConvolution
Date of creation 2013-03-22 14:28:26
Last modified on 2013-03-22 14:28:26
Owner swiftset (1337)
Last modified by swiftset (1337)
Numerical id 4
Author swiftset (1337)
Entry type Definition
Classification msc 44A35
Synonym scale convolution
Related topic Convolution