Dynamical properties of endomorphisms, multiresolutions, similarity and orthogonality relations

Palle Jorgensen; Feng Tian

doi:10.3934/dcdss.2019146

Back

Dynamical properties of endomorphisms, multiresolutions, similarity and orthogonality relations

Journal article

Open access

Dynamical properties of endomorphisms, multiresolutions, similarity and orthogonality relations

Palle Jorgensen and Feng Tian

Discrete and continuous dynamical systems. Series S, Vol.12(8), pp.2307-2348

2019

DOI: 10.3934/dcdss.2019146

Files and links (1)

url

https://doi.org/10.3934/dcdss.2019146View

Published (Version of record) Open Access

Abstract

We study positive transfer operators R in the setting of general measure spaces (X,B). For each R, we compute associated path-space probability spaces (Ω,P). When the transfer operator R is compatible with an endomorphism in (X,B), we get associated multiresolutions for the Hilbert spaces L2(Ω,P) where the path-space Ω may then be taken to be a solenoid. Our multiresolutions include both orthogonality relations and self-similarity algorithms for standard wavelets and for generalized wavelet-resolutions. Applications are given to topological dynamics, ergodic theory, and spectral theory, in general; to iterated function systems (IFSs), and to Markov chains in particular.

Details

Title: Subtitle: Dynamical properties of endomorphisms, multiresolutions, similarity and orthogonality relations
Creators: Palle Jorgensen
Feng Tian
Resource Type: Journal article
Publication Details: Discrete and continuous dynamical systems. Series S, Vol.12(8), pp.2307-2348
DOI: 10.3934/dcdss.2019146
ISSN: 1937-1179
eISSN: 1937-1179
Language: English
Date published: 2019
Academic Unit: Mathematics
Record Identifier: 9983986085902771

Metrics

16 Record Views

4 Times Cited - Web of Science