ABSTRACT
Thus the expansion of / converges in the sense of S'r to some fo G i.e.,
But the convergence of the expansion of / is much stronger than this since ^an(f)(t — n) converges uniformly on bounded sets as do its first r derivatives. This follows from the inequality
In fact we have shown that the limiting function and its r derivatives are continuous functions of polynomial growth on R. These results enable us to imitate the multiresolution analysis of L2(R) in S'r.
