TCHAPAIEV

You need to find an "f" corresponding to Gw2*f; clearly the only candidate is just NOT the function I ( equal to 1 everywhere ) BUT the step function which is the caracateristic function of [a,b] that means the function equal to 1 on [a,b] and 0 elsewhere ! Intuition for convolution is easy by practicing it is a remarquale tool which allow to FOURIER TRANSFORM in one click ; * becomes just ordinary product of functions ( the Fourier transform of ........ ) in case of the gaussian the forier transform is almost identical to itself ; so what remains is to compute the Fourier transfrorm of the indicatrice of the intreval [a, b]; What do you expect preicely by "more intuition" there are a lot of books for students ;all which are relied to convolution are related to Fourier transforms ans series ; please have some look to those