I have the following relation
$$f(x)=\int_{-\infty}^{\infty}a(x,u)\,\frac{1}{\sqrt{2\pi u}}\,\exp\left(-\frac{h^2}{2u}\right)\,du.$$
How do I find the expression for $a(x,u)$ from this?
My attempt: The integral on LHS looks like the Laplace transform in $\dfrac{h^2}{2}$ if $u$ is replaced by $\dfrac{1}{u}$. I am not sure how to proceed further.