|Dept.||University of Colorado at Boulder|
We discuss a construction, first due to D. Dutkay and P. Jorgensen, that can be used to define generalized wavelets on inflated fractal spaces arising from iterated function systems. Self-similarity relations defining the fractal spaces also give rise to filter functions defined on the torus. These filter functions can be used to construct isometries, as well as probability measures on solenoids. Representations of the Baumslag-Solitar group can be obtained from the probability measures, and some properties of the representation are related to properties of the original wavelet and filter systems. The talk is based on joint work with L. Baggett, N. Larsen, K. Merrill, I. Raeburn, and A. Ramsay, and if time permits recent joint work with C. Farsi, E. Gillaspy and S. Kang concerning generalized wavelets related to representations of higher-rank graph algebras on fractal spaces will be discussed.