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Low-pass filters and representations of the Baumslag Solitar group
Author(s):
Dorin
Ervin
Dutkay
Journal:
Trans. Amer. Math. Soc.
358
(2006),
5271-5291.
MSC (2000):
Primary 42C40, 28A78, 46L45, 28D05, 22D25
Posted:
July 21, 2006
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Abstract:
We analyze representations of the Baumslag Solitar group that admit wavelets and show how such representations can be constructed from a given low-pass filter. We describe the direct integral decomposition for some examples and derive from it a general criterion for the existence of solutions for scaling equations. As another application, we construct a Fourier transform for some Hausdorff measures.
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Additional Information:
Dorin
Ervin
Dutkay
Affiliation:
Department of Mathematics, Hill Center-Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019
Email:
ddutkay@math.rutgers.edu
DOI:
10.1090/S0002-9947-06-04230-9
PII:
S 0002-9947(06)04230-9
Keywords:
Wavelet,
representation,
low-pass filter,
scaling function,
Baumslag Solitar group,
solenoid,
decomposition,
ergodic action,
fractal
Received by editor(s):
July 21, 2004
Posted:
July 21, 2006
Additional Notes:
This work was supported in part by NSF grant DMS0457491
Copyright of article:
Copyright
2006,
American Mathematical Society
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