A direct integral decomposition of the wavelet representation
Authors:
LekHeng Lim, Judith A. Packer and Keith F. Taylor
Journal:
Proc. Amer. Math. Soc. 129 (2001), 30573067
MSC (2000):
Primary 65T60, 47N40, 22D20, 22D30; Secondary 22D45, 47L30, 47C05
Published electronically:
April 16, 2001
MathSciNet review:
1840112
Fulltext PDF Free Access
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Abstract: In this paper we use the concept of wavelet sets, as introduced by X. Dai and D. Larson, to decompose the wavelet representation of the discrete group associated to an arbitrary integer dilation matrix as a direct integral of irreducible monomial representations. In so doing we generalize a result of F. Martin and A. Valette in which they show that the wavelet representation is weakly equivalent to the regular representation for the BaumslagSolitar groups.
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 L. Baggett, H. Medina and K. Merrill, ``Generalized multiresolution analyses, and a construction procedure for all wavelet sets in ,'' J. Fourier Anal. Appl. 5, 1999, pp. 563573. CMP 2000:11
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 B. Brenken, ``The local product structure of expansive automorphisms of solenoids and their associated algebras,'' Canad. J. Math., 48 (4), 1996, pp. 692709. MR 98c:22003
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 B. Brenken and P. Jorgensen, ``A family of dilation crossed product algebras,'' J. Operator Theory, 25, 1991, pp. 299308. MR 94m:46103
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Additional Information
LekHeng Lim
Affiliation:
Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 148534201
Address at time of publication:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
Email:
lekheng@math.cornell.edu
Judith A. Packer
Affiliation:
Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260
Email:
matjpj@leonis.nus.edu.sg
Keith F. Taylor
Affiliation:
Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan, Canada S7N 5E6
Email:
taylor@math.usask.ca
DOI:
http://dx.doi.org/10.1090/S0002993901059287
PII:
S 00029939(01)059287
Keywords:
Wavelet,
wavelet set,
group representations
Received by editor(s):
November 15, 1999
Received by editor(s) in revised form:
February 24, 2000
Published electronically:
April 16, 2001
Additional Notes:
The third author was supported in part by a grant from NSERC Canada.
Communicated by:
David R. Larson
Article copyright:
© Copyright 2001
American Mathematical Society
