Wavelets for iterated function systems

We construct a wavelet and a generalised Fourier basis with respect to some fractal measure given by a one-dimensional iterated function system In this paper we will not assume that these systems are given by linear contractions generalising in this way some previous work of Dutkay, Jorgensen, and Pedersen to the non-linear setting As a byproduct we ale able to provide a Fourier basis also for such linear fractals like the Middle Third Cantor Set which have been left out by previous approaches (C) 2010 Elsevier Inc. All rights reserved