The convolution of the function e^{-|x|} results in (1-x)e^{x} for x<0 and (1+x)e^{-x} for x>0. The integral must be evaluated over the appropriate intervals without taking limits as x approaches positive or negative infinity. A common mistake is assuming the convolution evaluates to zero, which can occur if the absolute values are not correctly handled in the integral setup.
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Unredeemed said:Homework Statement
Prove that the convolution of e^{-\left|x\right|} is (1-x)e^{x} for x<0 and (1+x)e^{-x} for x>0
Homework Equations
The Attempt at a Solution
I plug through the integral in the standard way and take the limits as x tends to positive and negative infinity etc. But, I keep getting that the convolution is zero?
Any help would be greatly appreciated.