Logarithmic convolution: Difference between revisions

Revision as of 02:01, 15 September 2024

Revision as of 02:22, 15 September 2024

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{{unreferenced |date= October 2010}}

In [[mathematics]], the '''scale convolution''' of two [[Function (mathematics)|functions]] <math>s(t)</math> and <math>r(t)</math>, also known as their '''logarithmic convolution''' is defined as the function{{cn|date=September 2024}}

:<math> s *_l r(t) = r *_l s(t) = \int_0^\infty s\left(\frac{t}{a}\right)r(a) \, \frac{da}{a}</math>

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==Results==

The logarithmic convolution can be related to the ordinary [[convolution]] by changing the [[Variable (mathematics)|variable]] from <math>t</math> to <math>v = \log t</math>:{{cn|date=September 2024}}

: <math>\begin{align}