Representation theory and multilevel filters

Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
JournalJournal of Applied Mathematics and Computing
DOIs
StateAccepted/In press - 1 Jan 2022

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

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