  We consider the class $PW(\mathbb R^n)$ of functions in $L^2(\mathbb R^n)$,
whose Fourier transform has bounded support. We obtain a description of
continuous maps $\varphi : \mathbb R^m\rightarrow\mathbb R^n$ such that
$f\circ\varphi\in PW(\mathbb R^m)$ for every function $f\in PW(\mathbb R^n)$.
Only injective affine maps $\varphi$ have this property.

Classical Analysis and ODEs