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Irreducible Wavelet Representations and Ergodic Automorphisms on Solenoids

Dutkay, Dorin Ervin; Larson, David R. and Silvestrov, Sergei LU (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.
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author
organization
publishing date
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
2011-07-06 15:17:32
date last changed
2017-01-01 05:53:41
@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},
  keyword      = {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},
}