(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove the associativity law and the distributive law for convolution:

(1) prove F*(G+H)=(F*G)+(F*H)

(2) prove: F*(G*H)=(F*G)*H

2. Relevant equations

3. The attempt at a solution

(1) proof: using the definition of the laplace using convolution

Left hand side: =integral(F(u)(G(t-u)+H(t-u))du

=laplace(F)xlaplace(G)+Laplace(F)xlaplace(H)

Right hand side: =integral(F(u)G(t-u))du + integral(F(u)H(t-u)du

=laplace(F)xlaplace(G)+laplace(F)laplace(H) = left hand side

I dont know how to prove the second one. Any help would be v much appreciated.

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# Laplace convolution properties

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