I struggled lots of time about following problem, but I don't know how to prove following statement.
for $f \in C_0(\mathbb{R}) \ \cap\ L^1(\mathbb{R})$, there exist $A > 0$ such that $\left|\hat{f}(w)\right| \leq \frac{A}{W} \forall w \in \mathbb{R} \backslash 0$. ($\hat{f}$ is not necessarily integrable).
Prove that:
$$f(x) = \frac{1}{2\pi}\int_{-\infty}^{+\infty}\hat{f}(w) e^{iwx} dw $$
How can i prove this statement?
