I am trying to find out the convolution of the following two functions using integration but I got stuck. Please help!
Consider the following functions on $\mathbb R^n$:
$$f(x) = e^{-a|x|^2}, \ \ \ \ \ g(x) = e^{-b|x|^2}.$$
I am trying to find $f \ast g$ using the basic definition of the convolution:
$$(f \ast g ) (x) = \int_{\mathbb R^n} f(y)g(x-y) dy $$
My try : I tried to write the $|x|^2$ as a sum of its sqaured components and did similarly for the $|y|^2 $ but I am struggling with how to integrate the product i receive after doing this in side the integral.