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As stated in this article, the Weierstrass transform of $f(x)$ is defined as: \begin{equation} W[f](x)=\frac{1}{4\pi}\int_{-\infty}^{\infty}f(y)e^{-\frac{(x-y)^{2}}{4}}dy \end{equation} which can be ...

Consider the following partial differential equation with an initial condition $u(x,0)=f(x)$: \begin{equation} \frac{\partial}{\partial t} u(x,t)=g_{1}(x)\frac{\partial u}{\partial x}+g_{2}(x)\frac{\...