On some properties of convolution

59 Views Asked by Bumbble Comm At 09 Apr 2026 - 7:42

Let $f(x)=e^{-x^2}.$ Can we find a function $g$ such that $f*g$ is well-defined, not identically zero and not supported on whole real line?

Note that if $f(x)=1$ then we can't find any such $g$.

($f*g$ denotes the convolution of $f,g$)

My try: enter image description here