  Let $L$ be a proper differentiation invariant subspace of $C^\infty(a,b)$
such that the restriction operator $\frac{d}{dx}\bigl{|}_L$ has a discrete
spectrum $\Lambda$ (counting with multiplicities). We prove that $L$ is spanned
by functions vanishing outside some closed interval $I\subset(a,b)$ and
monomial exponentials $x^ke^{\lambda x}$ corresponding to $\Lambda$ if its
density does not exceed the critical value $\frac{|I|}{2\pi}$, and moreover, we
show that the result is not necessarily true when the density of $\Lambda$
equals the critical value. This answers a question posed by the first author
and B. Korenblum. Finally, if the residual part of $L$ is trivial, then $L$ is
spanned by the monomial exponentials it contains.
