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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Parametrizing smooth compactly supported wavelets


Author: Raymond O. Wells
Journal: Trans. Amer. Math. Soc. 338 (1993), 919-931
MSC: Primary 42C15
DOI: https://doi.org/10.1090/S0002-9947-1993-1107031-8
MathSciNet review: 1107031
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Abstract: In this paper a concrete parameter space for the compactly supported wavelet systems of Daubechies is constructed. For wavelet systems with $ N$ (generic) nonvanishing coefficients the parameter space is a closed convex set in $ {{\mathbf{R}}^{(N - 2)/2}}$, which can be explicitly described in the Fourier transform domain. The moment-free wavelet systems are subsets obtained by the intersection of the parameter space and an affine subspace of $ {{\mathbf{R}}^{(N - 2)/2}}$.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1107031-8
Article copyright: © Copyright 1993 American Mathematical Society