The compactly supported cardinal orthogonal vector-valued wavelets with dilation factor α

In this paper, we firstly introduce vector-valued multiresolution analysis with dilation factor α ⩾ 2 and orthogonal vector-valued wavelet. Then, we consider the existence of cardinal compactly supported orthogonal vector-valued wavelet system and describe the characterization of compactly supported...

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Bibliographic Details
Published in:Applied mathematics and computation 2008-11, Vol.205 (1), p.309-316
Main Authors: Liu, Hongjie, Feng, Boqin, Wu, Guochang
Format: Article
Language:English
Subjects:
Differential geometry
Exact sciences and technology
Fourier analysis
Geometry
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Operator theory
Orthogonal cardinal vector-valued scaling function
Orthogonal vector-valued wavelet
Sciences and techniques of general use
Vector-valued multiresolution analysis
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Summary:In this paper, we firstly introduce vector-valued multiresolution analysis with dilation factor α ⩾ 2 and orthogonal vector-valued wavelet. Then, we consider the existence of cardinal compactly supported orthogonal vector-valued wavelet system and describe the characterization of compactly supported orthogonal cardinal vector-valued scaling function and orthogonal vector-valued wavelet. In special, we give some characterizations of cardinal orthogonal vector-valued wavelet system by its mask and symbol in L 2 ( R , C 2 ) . According to Theorems in Section 3, we can conclude algorithm about constructing compactly supported cardinal orthogonal vector-valued wavelet. At last, we give some examples to illustrate our algorithm.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2008.08.032