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Some generalized method for constructing nonseparable compactly supported wavelets in $L^2(mathbb{R}^2)$

Author(s): Wojciech Banaś

Journal: Opuscula Mathematica
ISSN 1232-9274

Volume: 33;
Issue: 2;
Start page: 223;
Date: 2013;
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Keywords: compactly supported wavelet | compactly supported scaling function | multiresolution analysis | dilation matrix | orthonormality | accuracy

In this paper we show some construction of nonseparable compactly supported bivariate wavelets. We deal with the dilation matrix $A = iny{left[egin{matrix}0 & 2 cr 1 & 0 cr end{matrix} ight]}$ and some three-row coefficient mask; that is a scaling function satisfies a dilation equation with scaling coefficients which can be contained in the set ${c_{n}}_{n inmathcal{S}},$ where $mathcal{S}=S_{1} imes {0,1,2},$ $S_{1} subset mathbb{N},$ $sharp S_{1} < infty.$
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