Construction of orthogonal multi-wavelets using generalized-affine fractal interpolation functions

We present a new construction of fractal interpolation surfaces defined on arbitrary rectangular lattices. We use this construction to form finite sets of fractal interpolation functions (FIFs) that generate multiresolution analyses of L2(ℝ²) of multiplicity r. These multiresolution analyses are based on the dilation properties of the construction. The associated multi-wavelets are orthogonal and discontinuous functions. We give concrete examples to illustrate the method and generalize it to form multiresolution analyses of L2(ℝ^d), d > 2. To this end, we prove some results concerning the Hölder exponent of FIFs defined on [0, 1]^d.