## A tricky integral equation

In the context of reconstruction of climate data from ice cores (see related question at MSE) I came about the following problem. (More background and motivation can be given on demand.) Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be an arbitrary smooth function, and let $p(x)$ be a probability function with $\int_{-\infty}^{\infty} p(x)\text{d}x = 1$. We can write: $$\int_{-\infty}^{\infty} … Read more