Prove Equivalence of Two Functions - Convolution Identity

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SUMMARY

The discussion centers on proving the equivalence of two functions related to convolution identity, specifically G(2t-τ1-τ2) = G(t-τ1) G(t-τ2)/c. The user has confirmed their equivalence through numerical checks but struggles with the analytical proof, particularly with the double integral involved. The challenge lies in simplifying the double integral into a single integral expression, which remains unresolved. Assistance is sought to navigate this analytical proof process.

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muzialis
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Hi there,
working on a physical problem I found two functions that should be equivalent, and indeed they seem to be after a numerical check.

The functions are shown in the attached PDF. I can not figure a way to prove their equivalence analytically (the double integral especially gives me grief when trying to "unravel" it, to get to a single integral expression)
Any help would be so appreciated, thank you very much
 

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G(2t-τ1-τ2) = G(t-τ1) G(t-τ2)/c
The double integral then factors into two separate integrals which are identical in effect.
 

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