Journal article
Measurable multiresolution systems, endomorphisms, and representations of Cuntz relations
Quantum Studies : Mathematics and Foundations, Vol.11(1), pp.87-116
04/2024
DOI: 10.1007/s40509-024-00319-6
Abstract
The purpose of this paper is to present new classes of function systems as part of multiresolution analyses. Our approach is representation theoretic, and it makes use of generalized multiresolution function systems (MRSs). It further entails new ideas from measurable endomorphisms dynamics. Our results yield applications that are not amenable to more traditional techniques used on metric spaces. As the main tool in our approach, we make precise new classes of generalized MRSs which arise directly from a dynamical theory approach to the study of surjective endomorphisms on measure spaces. In particular, we give the necessary and sufficient conditions for a family of functions to define generators of Cuntz relations. We find an explicit description of the set of generalized wavelet filters. Our results are motivated in part by analyses of sub-band filters in signal/image processing. But our paper goes further, and it applies to such wider contexts as measurable dynamical systems and complex dynamics. A unifying theme in our results is a new analysis of endomorphisms in general measure space, and its connection to multi-resolutions, to representation theory, and generalized wavelet systems.
Details
- Title: Subtitle
- Measurable multiresolution systems, endomorphisms, and representations of Cuntz relations
- Creators
- Sergey Bezuglyi - University of IowaPalle E. T. Jorgensen - Univ Iowa, Iowa City, IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Quantum Studies : Mathematics and Foundations, Vol.11(1), pp.87-116
- Publisher
- Springer Nature
- DOI
- 10.1007/s40509-024-00319-6
- ISSN
- 2196-5609
- eISSN
- 2196-5617
- Number of pages
- 30
- Language
- English
- Electronic publication date
- 02/08/2024
- Date published
- 04/2024
- Academic Unit
- Mathematics
- Record Identifier
- 9984560208002771
Metrics
1 Record Views