Self-affine fractal functions and wavelet series

[摘要] We consider functions represented by series Sigma(g is an element of G) c(g)psi(g(-1)(x)) of wavelet-type, where G is a group generated by affine functions L-1,..., L-n and psi 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. (C) 1999 Academic Press.

[发布日期] 1999-12-15

[关键词] fractals;wavelets;functional equations;Holder exponents