Originally Posted by

**Deadstar** Given that f is a function of moderate decrease, $\displaystyle \hat{f}(\xi)$ is continuous and also satisfies,

$\displaystyle |\hat{f}(\xi)| \leq \frac{C}{|\xi|^{1+\alpha}}$.

Use the inversion theorem to derive an expression for $\displaystyle f(x+h) - f(x)$. It should be in the form of an integral.

How would I do this? Would I use a change of variable?

Just typed out long possible solution but then realized inversion theorem is $\displaystyle d \xi$ not $\displaystyle dx$...