Paley-Wiener space

A function $$f\in L^{2}(\mathbb R)$$ is band-limited if the Fourier transform $$\hat f$$ has compact support.

The Paley-Wiener space, $$PW$$, is the space of functions whose Fourier transform has compact support:

$$PW = :\{f\in L^2(\mathbb R) | \text{ supp}\hat{f} \subseteq [-\frac{1}{2}, \frac{1}{2}]\}$$