Irreducible Wavelet Representations and Ergodic Automorphisms on Solenoids
(2011) In Operators and Matrices 5(2). p.201-219- Abstract
- We focus on the irreducibility of wavelet representations. We present some connections between the following notions: covariant wavelet representations, ergodic shifts on solenoids, fixed points of transfer (Ruelle) operators and solutions of refinement equations. We investigate the irreducibility of the wavelet representations, in particular the representation associated to the Cantor set, introduced in [13], and we present several equivalent formulations of the problem.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1985245
- author
- Dutkay, Dorin Ervin ; Larson, David R. and Silvestrov, Sergei LU
- organization
- publishing date
- 2011
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Representation, ergodic automorphism, Cantor set, Ruelle operator, solenoid, refinable function
- in
- Operators and Matrices
- volume
- 5
- issue
- 2
- pages
- 201 - 219
- publisher
- Element
- external identifiers
-
- wos:000291111800002
- scopus:79955959997
- ISSN
- 1846-3886
- language
- English
- LU publication?
- yes
- id
- 128eb7dc-2b38-4fa1-b523-2d2fcea9a0e4 (old id 1985245)
- date added to LUP
- 2016-04-01 13:48:56
- date last changed
- 2022-01-27 21:16:04
@article{128eb7dc-2b38-4fa1-b523-2d2fcea9a0e4, abstract = {{We focus on the irreducibility of wavelet representations. We present some connections between the following notions: covariant wavelet representations, ergodic shifts on solenoids, fixed points of transfer (Ruelle) operators and solutions of refinement equations. We investigate the irreducibility of the wavelet representations, in particular the representation associated to the Cantor set, introduced in [13], and we present several equivalent formulations of the problem.}}, author = {{Dutkay, Dorin Ervin and Larson, David R. and Silvestrov, Sergei}}, issn = {{1846-3886}}, keywords = {{Representation; ergodic automorphism; Cantor set; Ruelle operator; solenoid; refinable function}}, language = {{eng}}, number = {{2}}, pages = {{201--219}}, publisher = {{Element}}, series = {{Operators and Matrices}}, title = {{Irreducible Wavelet Representations and Ergodic Automorphisms on Solenoids}}, volume = {{5}}, year = {{2011}}, }