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

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 20 August 2005. For the current production of this journal, please refer to http://www.math.psu.edu/era/.

This journal is archived by the American Mathematical Society. The master copy is available at http://www.ams.org/era/

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

Abderrazek Karoui

Abstract.

In this note, we announce a general method for the construction of nonseparable orthogonal wavelet bases of $L^2(\R^n)$, 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.

Retrieve entire article

TeX source

DVI

PostScript

Article Info

ERA Amer. Math. Soc. 09 (2003), pp. 32-39
Publisher Identifier: S 1079-6762(03)00109-4
2000 Mathematics Subject Classification. Primary 39B42, 42C05; Secondary 42C15
Key words and phrases. Multidimensional wavelet bases, multiwavelet bases, refinement equation, stability
Received by editors December 14, 2001
Posted on April 4, 2003
Communicated by Guido Weiss
Comments (When Available)

Abderrazek Karoui

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

E-mail address: abkaroui@yahoo.com

Electronic Research Announcements of the AMS Home page