Laplace transform of convolution

Theorem.  If




Proof.  According to the definition of Laplace transformMathworldPlanetmath, one has


where the right hand side is a double integral over the angular region bounded by the lines  τ=0  and  τ=t  in the first quadrant of the tτ-plane.  Changing the of integration, we write


Making in the inner integral the substitution  t-τ:=u,  we obtain





Title Laplace transform of convolution
Canonical name LaplaceTransformOfConvolution
Date of creation 2013-03-22 18:24:04
Last modified on 2013-03-22 18:24:04
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 6
Author pahio (2872)
Entry type Theorem
Classification msc 26A42
Classification msc 44A10
Synonym convolution property of Laplace transform
Related topic Convolution