  We define an affine structure on $\ltwor\oplus...\oplus\ltwor$ and, following
some ideas developed in \cite{Dut1}, we construct a local trace function for
this situation. This trace function is a complete invariant for a shift
invariant subspace and it has a variety of properties which make it easily
computable. The local trace is then used to give a characterization of
super-wavelets and to analyze their multiplicity function, dimension function
and spectral function. The "$n\times$" oversampling result of Chui and Shi
\cite{CS} is refined to produce super-wavelets.
