# Fouriertransformation, equation

Hi,

I've got some problems on the following:

Let $$f:\mathbb{R} \to \mathbb{R}$$ be a twice differentiable function with $$\lim_{x \to \infty} \frac{|f(x)|}{|x^2|}=0$$ and $$\int_{-\infty}^{\infty} |f''(x)| dx$$ is bounded.
Let
$$F(y) = \int_{-\infty}^{\infty} f(x) e^{-2 \pi ixy} dx$$
be the Fourier transform of $$f$$.

Then:

$$\sum_{n = -\infty}^{\infty} f(n) = \sum_{m = -\infty}^{\infty} F(m)$$

holds.

For sure I can insert the Fourier transform of $$f$$ into the sum - but I don't see how to continue. Actually I assume it's a quite easy thing if one sees it... unfortunately I don't :(

Dick