For a certain application I need to compute a pointwise supremum of this family of gaussian convolutions:
$$\sup_s f(x)\otimes e^{-\frac{x^2}{s^2}}$$
where $f(x),x\in \mathbb{R}^2$ is known and $\otimes$ is a convolution over the entire plane.
Could you point me to a reference that would help with computation of this envelope of parametrized convolutions?
