Logarithmic convolution
id:
logarithmic-convolution-230-1743949
title:
Logarithmic convolution
text:
In mathematics, the scale convolution of two functions s and r, also known as their logarithmic convolution or log-volution is defined as the function
- s ∗ l r = r ∗ l s = ∫ 0 ∞ s r d a a when this quantity exists. The logarithmic convolution can be related to the ordinary convolution by changing the variable from t to v = log t :
- s ∗ l r = ∫ 0 ∞ s r d a a = ∫ − ∞ ∞ s r d u = ∫ − ∞ ∞ s r d u. Define f = s and g = r and let v = log t, then
- s ∗ l r = f ∗ g = g ∗ f = r ∗ l s.
brand slug:
wiki
category slug:
encyclopedia
description:
original url:
https://en.wikipedia.org/wiki/Logarithmic_convolution
date created:
2006-08-12T12:42:18Z
date modified:
2024-09-15T16:44:56Z
main entity:
{"identifier":"Q6667306","url":"https://www.wikidata.org/entity/Q6667306"}
image:
fields total:
13
integrity:
14