Hello!

$\displaystyle F := \{f \in L^2(\mathbb{R}) : \int^\infty_{-\infty} (1+x^2)|\hat{f}(x)|^2 dx < \infty \}$

($\displaystyle \hat{f}$ fourier transform)

is a normed space.

Show that $\displaystyle dim(F) < \infty$

I really don't know how to do this. Usually you find n basis vectors of X => dim(X) = n. But I find it pretty hard, anyone got some ideas? Any help would be much appreciated.

Thank you,

Rapha