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

*Copyright 2003 American Mathematical Society*

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#### 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`

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