Representation Theory and Multilevel Filters
We present a general setting where wavelet filters and multiresolution decompositions can be defined, beyond the classical L2(R, dx) setting. This is done in a framework of iterated function system (IFS) measures; these include all cases studied so far, and in particular the Julia set/measure cases. Every IFS has a fixed order, say N, and we show that the wavelet filters are indexed by the infinite dimensional group G of functions from X into the unitary group UN. We call G the loop group because of the special case of the unit circle.
Alpay, D., Jorgensen, P. & Lewkowicz, I. Representation theory and multilevel filters. J. Appl. Math. Comput. (2022). https://doi.org/10.1007/s12190-022-01805-z