Generalized Self-similarity, Wavelets and Image Analysis

We present a solution to a functional equation by means of the construction of a contractive operator on some functional space. This solutions presents a kind of self-similarity and enables us to generalize the model introduced by Cabrelli et al. in CFMV92] allowing a much greater exibility. In particular dilation equations of the type f (x) = P c k f (2x ? k) t into this model, and hence we can construct a multiresolution analysis in the sense of Mallat and Meyer. On the other hand, this \generalized self-similarity" notion provides us with a method for the construction of an operator whose xed point is close to a given target.