Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 1599-1657 |
Number of pages | 59 |
Journal | Journal of Applied Mathematics and Computing |
Volume | 69 |
Issue number | 2 |
DOIs | |
State | Published - 1 Apr 2023 |
Keywords
- Algorithms
- Cuntz algebra
- Factorization
- Iterated function system
- Matrix-valued functions
- Multi resolution
- Rational functions
- Representation
- Solenoid
- Transfer operator
- Wavelet decomposition
- Wavelet filters
- Weighted composition operator
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics