  This paper has the characteristics of a review paper in which results of
shift-invariant subspaces of Sobolev type are summarized without proofs. The
structure of shift-invariant spaces $V_s$, $s\in\mathbb{R}$, generated by at
most countable family of generators, which are subspaces of Sobolev spaces
$H^s(\mathbb{R}^n)$, are announced in \cite{aap} and Bessel sequences, frames
and Riesz families of such spaces are characterized. With the Fourier
multiplier
$\left(1-\frac{\Delta}{4\pi^2}\right)^{s/2}f=\mathcal{F}^{-1}\big((1+|t|^2)^{s/2}\widehat{f}(t)\big)$,
we are able to extend notions and theorems in \cite{MB} to spaces of the
Sobolev type.
