A note on the construction of nonseparable wavelet bases and multiwavelet matrix filters of 𝐿²(ℝⁿ), where 𝕟≥2

Karoui, Abderrazek

doi:10.1090/S1079-6762-03-00109-4

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
DOI: https://doi.org/10.1090/S1079-6762-03-00109-4
Published electronically: April 4, 2003
MathSciNet review: 1988870
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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.

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