Cuntz-Krieger algebras and wavelets on fractals

TL;DR

This paper constructs wavelets on fractal Cantor sets using representations of Cuntz-Krieger algebras and associated operators, bridging operator algebras and fractal analysis.

Contribution

It introduces a novel method to build wavelets on fractals via Cuntz-Krieger algebra representations and Perron-Frobenius operators.

Findings

Wavelet families are successfully constructed on Cantor sets.

The approach links operator algebra representations with fractal wavelet analysis.

Potential applications in fractal signal processing and analysis.

Abstract

We consider representations of Cuntz--Krieger algebras on the Hilbert space of square integrable functions on the limit set, identified with a Cantor set in the unit interval. We use these representations and the associated Perron-Frobenius and Ruelle operators to construct families of wavelets on these Cantor sets.