this is fredholm type of integral equation that im currently triying to solve
$$\int_{-\infty}^{\infty}e^{-(t-x)^2}\phi(t)dt=e^{-x^2/8}$$
the question is that how to derive $\phi(t)$
i tried convolution theorem of fourier transform to solve this equation
and what i got is $ \phi(t)=\sqrt{8\over7\pi}e^{-t^2\over7}$
but it seems suspicious.. is it correct answer?