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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Parametrizing smooth compactly supported wavelets
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by Raymond O. Wells PDF
Trans. Amer. Math. Soc. 338 (1993), 919-931 Request permission


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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  • A. Haar, Math. Ann. 69 (1910), 336.
  • Wayne M. Lawton, Tight frames of compactly supported affine wavelets, J. Math. Phys. 31 (1990), no. 8, 1898–1901. MR 1067632, DOI 10.1063/1.528688
  • D. Pollen, Parametrization of compactly supported wavelets, Company Report, Aware, Inc., AD890503.1.4, May, 1989.
  • Georg Pólya and Gabor Szegő, Aufgaben und Lehrsätze aus der Analysis. Band II: Funktionentheorie, Nullstellen, Polynome Determinanten, Zahlentheorie, Heidelberger Taschenbücher, Band 74, Springer-Verlag, Berlin-New York, 1971 (German). Vierte Auflage. MR 0344041
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 338 (1993), 919-931
  • MSC: Primary 42C15
  • DOI:
  • MathSciNet review: 1107031