Multiresolution analyses based on fractal functions

AbstractWe use a finite set of fractal interpolation functions to generate multiresolution analyses on L2(R) and C0(R). These multiresolution analyses rely on the properties of fractal functions such as self-affiniteness, existence of scaled coupled dilation equations, and the non-integral box dimension of their graph. This dimension serves as an additional parameter to better describe the small-scale structure of the set to be approximated. Concrete examples will be given to illustrate these methods