A direct integral decomposition of the wavelet representation

Authors:
Lek-Heng Lim, Judith A. Packer and Keith F. Taylor

Journal:
Proc. Amer. Math. Soc. **129** (2001), 3057-3067

MSC (2000):
Primary 65T60, 47N40, 22D20, 22D30; Secondary 22D45, 47L30, 47C05

DOI:
https://doi.org/10.1090/S0002-9939-01-05928-7

Published electronically:
April 16, 2001

MathSciNet review:
1840112

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 Baumslag-Solitar groups.

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Additional Information

**Lek-Heng Lim**

Affiliation:
Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853-4201

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:
https://doi.org/10.1090/S0002-9939-01-05928-7

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