Wavelets for iterated function systems

TL;DR

This paper develops wavelet and Fourier basis constructions for fractal measures generated by nonlinear iterated function systems, extending previous linear-based methods to a more general nonlinear context.

Contribution

It introduces a new framework for wavelet and Fourier basis construction on fractals from nonlinear iterated function systems, broadening the scope of prior linear approaches.

Findings

Constructed wavelet bases for nonlinear fractal measures

Extended Fourier basis methods to nonlinear IFS measures

Generalized previous linear IFS wavelet constructions

Abstract

We construct a wavelet and a generalised Fourier basis with respect to some fractal measures given by one-dimensional iterated function systems. In this paper we will not assume that these systems are given by linear contractions generalising in this way some previous work of Jorgensen and Dutkay to the non-linear setting.