C. Cabrelli, U. Molter. Generalized self-similarity, wavelets and image analysis. Preprint 78, Dept. of Math, University of Buenos Aires, 1994.
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 flexibility. In particular dilation equations of the type f(x) = ( ck f(2x-k) fit 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 fixed point is close to a given target.
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@Misc{CaMo94,
Author = {Cabrelli, C. and Molter, U.},
Title = {Generalized self-similarity, wavelets and image analysis},
Howpublished = {Preprint 78, Dept. of Math, University of Buenos Aires},
Year = {1994}
}