Self-Affine Fractal Functions and Wavelet Series

We consider functions represented by series C, c, $(g- ʹ(x)) of wavelet-type, where G is a group generated by affine functions L,, . . . , L, and $ is piecewise affine. By means of those functions we characterize the class of self-affine fractal functions, previously studied by Barnsley et al. We compute their global and local Holder exponents and investigate points of non-differentiability. Wavelet-representations for various continuous nowhere differentiable and singular functions are presented. Another application is the construction of functions with prescribed local Holder exponents at each point