UCLA

\begin{abstract} Multiresolution Approximation subspaces are $\L^2(\RR)$-subspaces defined for each scale over all time-shifts, i.e., ``scale subspaces'', while with respect to a given wavelet, the signal space $\L^2(\RR)$ not only admits orthogonal scale subspaces basis, but orthogonal ``time-shift subspaces'' basis as well. It is therefore natural to expect both scale subspaces and time-shift subspaces to play a role in Wavelet Theory and, in particular, in Multiresolution Approximation as well. This is what will be shown in the paper. \end{abstract}