Decomposition of wavelet representations and Martin boundaries

Research output: Contribution to journalArticle

Abstract

We study a decomposition problem for a class of unitary representations associated with wavelet analysis, wavelet representations, but our framework is wider and has applications to multi-scale expansions arising in dynamical systems theory for non-invertible endomorphisms. Our main results offer a direct integral decomposition for the general wavelet representation, and we solve a question posed by Judith Packer. This entails a direct integral decomposition of the general wavelet representation. We further give a detailed analysis of the measures contributing to the decomposition into irreducible representations. We prove results for associated Martin boundaries, relevant for the understanding of wavelet filters and induced random walks, as well as classes of harmonic functions. Published by Elsevier Inc.

Details

Authors
  • Dorin Ervin Dutkay
  • Palle E. T. Jorgensen
  • Sergei Silvestrov
Organisations
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • Irreducible representation, Wavelet, Martin boundary, Harmonic function
Original languageEnglish
Pages (from-to)1043-1061
JournalJournal of Functional Analysis
Volume262
Issue number3
Publication statusPublished - 2012
Publication categoryResearch
Peer-reviewedYes