Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

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,
  • 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
  • 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
  • 7. X. Wang, The study of wavelets from the properties of their Fourier transforms, Ph.D. Thesis, Washington University in St. Louis, 1995.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 41A15, 41A30, 42A38, 42C15, 46N99

Retrieve articles in all journals with MSC (1991): 41A15, 41A30, 42A38, 42C15, 46N99

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

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