Remote Access Electronic Research Announcements

Electronic Research Announcements

ISSN 1079-6762



A note on the construction of nonseparable wavelet bases and multiwavelet matrix filters of $L^2(\mathbb R^n)$, where $n\geq 2$

Author: Abderrazek Karoui
Journal: Electron. Res. Announc. Amer. Math. Soc. 9 (2003), 32-39
MSC (2000): Primary 39B42, 42C05; Secondary 42C15
Published electronically: April 4, 2003
MathSciNet review: 1988870
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this note, we announce a general method for the construction of nonseparable orthogonal wavelet bases of $L^2(\mathbb R^n),$ where $n\geq 2.$ Hence, we prove the existence of such type of wavelet bases for any integer $n\geq 2.$ Moreover, we show that this construction method can be extended to the construction of $n$-D multiwavelet matrix filters.

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

  • 1. A. Ayache, Construction of nonseparable dyadic compactly supported orthonormal wavelet bases for $L^2(\mathbb R^2)$ of arbitrarily high regularity, Rev. Math. Iberoamericana 15 (1999), 37-58. MR 2000b:42027
  • 2. W. He and M. Jun Lai, Construction of bivariate nonseparable compactly supported orthonormal multiwavelets with arbitrary high regularity, Preprint.
  • 3. H. Ji, S. D. Riemenschneider and Z. Shen, Multivariate compactly supported refinable functions, duals and biorthogonal wavelets, Studies in Applied Mathematics 102 (1999), 173-204. MR 99m:42049
  • 4. A. Karoui and R. Vaillancourt, Nonseparable biorthogonal wavelet bases of $L^2(\mathbb R^n)$, CRM Proceedings and Lecture Notes, Vol. 18, pp. 135-151, American Math. Society, Providence, RI, 1999. MR 99k:42061
  • 5. A. Karoui, A Technique for the construction of compactly supported biorthogonal wavelets of $L^2({\bf\mathbb R}^n), n\geq 2,$ J. Math. Anal. Appl. 249 (2000), 367-392. MR 2001h:42054
  • 6. A. Karoui, A general construction of nonseparable multivariate orthonormal wavelet bases and multidimensional multiwavelet matrix filters, Preprint.
  • 7. W. Lawton, S.L. Lee and Z. Shen, Stability and orthonormality of multivariate refinable functions, SIAM. J. Math. Anal. 28 (1997), 999-1014. MR 98d:41027
  • 8. Y. Meyer, Wavelets and Operators, Cambridge Studies in Advanced Mathematics, Vol. 37, Cambridge University Press, Cambridge, 1992. MR 94f:42001
  • 9. Z. Shen, Refinable function vectors, SIAM. J. Math. Anal. 29 (1998), 235-250. MR 99d:41038

Similar Articles

Retrieve articles in Electronic Research Announcements of the American Mathematical Society with MSC (2000): 39B42, 42C05, 42C15

Retrieve articles in all journals with MSC (2000): 39B42, 42C05, 42C15

Additional Information

Abderrazek Karoui
Affiliation: Université du 7 Novembre à Carthage, Institut Supérieur des Sciences Appliquées et de la Technologie de Mateur, 7030, Tunisia

Keywords: Multidimensional wavelet bases, multiwavelet bases, refinement equation, stability
Received by editor(s): December 14, 2001
Published electronically: April 4, 2003
Communicated by: Guido Weiss
Article copyright: © Copyright 2003 American Mathematical Society

American Mathematical Society