Cuntz-Krieger algebras and wavelets on fractals

Cuntz algebras representations have very interesting applications to wavelets, fractals and dynamical systems, see work by Bratteli, Jorgensen, Davidson et al. Some of these results have been extended to the more general class of Cuntz-Krieger algebras where the representations of these algebras are related to Perron-Frobenius operators of certain measure space transformations. In the talk I look at representations of the Cuntz-Krieger algebras on the Hilbert space of square integrable functions on the limit set identified with a Cantor set of the unit interval. These representations and the associated Perron-Frobenius and Ruelle operators are used to construct families of wavelets on these Cantor sets