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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the dimension function
of orthonormal wavelets


Author: Manos Papadakis
Journal: Proc. Amer. Math. Soc. 128 (2000), 2043-2049
MSC (1991): Primary 41A15, 41A30, 42A38, 42C15, 46N99
Published electronically: November 1, 1999
MathSciNet review: 1654108
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Abstract | References | Similar Articles | Additional Information

Abstract: We announce the following result: Every orthonormal wavelet of $L^2(\mathbf{R})$ is associated with a multiresolution analysis such that for the subspace $V_0$ the integral translates of a countable at most family of functions is a tight frame.


References [Enhancements On Off] (What's this?)

  • 1. Pascal Auscher, Solution of two problems on wavelets, J. Geom. Anal. 5 (1995), no. 2, 181–236. MR 1341029 (96g:42016), http://dx.doi.org/10.1007/BF02921675
  • 2. J. Benedetto, S. Li, The theory of multiresolution analysis frames and applications to filter banks, Appl. Comput. Harmon. Anal. 5 (1998), no. 4, 380-427. CMP 99:02
  • 3. L.W. Baggett, H.A. Medina, K.D. Merrill, Generalized multiresolution analyses and a construction procedure for all wavelet sets in $\mathbf{R}^n$, preprint, 1998.
  • 4. D. Han, D.R. Larson, Frames, bases and group representations, to appear Memoirs AMS.
  • 5. Eugenio Hernández and Guido Weiss, A first course on wavelets, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1996. With a foreword by Yves Meyer. MR 1408902 (97i:42015)
  • 6. Gustaf Gripenberg, A necessary and sufficient condition for the existence of a father wavelet, Studia Math. 114 (1995), no. 3, 207–226. MR 1338828 (96d:42049)
  • 7. X. Wang, The study of wavelets from the properties of their Fourier transforms, Ph.D. Thesis, Washington University in St. Louis, 1995.

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Additional Information

Manos Papadakis
Affiliation: Department of Informatics, University of Athens, Panepistimiopolis, GR-15784 Zografou, Greece
Address at time of publication: Department of Mathematics, University of Houston, Houston, Texas 77204-3476
Email: mpapad@di.uoa.gr, mpapadak@math.uh.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05256-9
PII: S 0002-9939(99)05256-9
Keywords: Multiresolution analysis, wavelets, dimension function, frames.
Received by editor(s): June 15, 1998
Received by editor(s) in revised form: August 25, 1998
Published electronically: November 1, 1999
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society