Wavelets on fractals.
We show that there are Hilbert spaces constructed from the Hausdorff measures H on the real line R with 0 < s < 1 which admit multiresolution wavelets. For the case of the middle-third Cantor set C ⊂ [0,1], the Hilbert space is a separable subspace of L(R, (dx)) where s = log(2). While we develop the general theory of multiresolutions in fractal Hilbert spaces, the emphasis is on the case of scale 3 which covers the traditional Cantor set C.