Orthogonal Multiwavelet Frames in L2Rd
We characterize the orthogonal frames and orthogonal multiwavelet frames in L2Rd with matrix dilations of the form (Df)(x)=detAf(Ax), where A is an arbitrary expanding d×d matrix with integer coefficients. Firstly, through two arbitrarily multiwavelet frames, we give a simple construction of a pair...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/846852 |
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| _version_ | 1832550188071256064 |
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| author | Liu Zhanwei Hu Guoen Wu Guochang |
| author_facet | Liu Zhanwei Hu Guoen Wu Guochang |
| author_sort | Liu Zhanwei |
| collection | DOAJ |
| description | We characterize the orthogonal frames and orthogonal multiwavelet frames in L2Rd with matrix dilations of the form (Df)(x)=detAf(Ax), where A is an arbitrary expanding d×d matrix with integer coefficients. Firstly, through two arbitrarily multiwavelet frames, we give a simple construction of a pair of orthogonal multiwavelet frames. Then, by using the unitary extension principle, we present an algorithm for the construction of arbitrarily many orthogonal multiwavelet tight frames. Finally, we give a general construction algorithm for orthogonal multiwavelet tight frames from a scaling function. |
| format | Article |
| id | doaj-art-09db609d96094435939780103bc6b65c |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-09db609d96094435939780103bc6b65c2025-02-03T06:07:24ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/846852846852Orthogonal Multiwavelet Frames in L2RdLiu Zhanwei0Hu Guoen1Wu Guochang2School of Information Engineering, Zhengzhou University, Zhengzhou 450001, ChinaDepartment of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou 450002, ChinaDepartment of Applied Mathematics, Henan University of Economics and Law, Zhengzhou 450002, ChinaWe characterize the orthogonal frames and orthogonal multiwavelet frames in L2Rd with matrix dilations of the form (Df)(x)=detAf(Ax), where A is an arbitrary expanding d×d matrix with integer coefficients. Firstly, through two arbitrarily multiwavelet frames, we give a simple construction of a pair of orthogonal multiwavelet frames. Then, by using the unitary extension principle, we present an algorithm for the construction of arbitrarily many orthogonal multiwavelet tight frames. Finally, we give a general construction algorithm for orthogonal multiwavelet tight frames from a scaling function.http://dx.doi.org/10.1155/2012/846852 |
| spellingShingle | Liu Zhanwei Hu Guoen Wu Guochang Orthogonal Multiwavelet Frames in L2Rd Journal of Applied Mathematics |
| title | Orthogonal Multiwavelet Frames in L2Rd |
| title_full | Orthogonal Multiwavelet Frames in L2Rd |
| title_fullStr | Orthogonal Multiwavelet Frames in L2Rd |
| title_full_unstemmed | Orthogonal Multiwavelet Frames in L2Rd |
| title_short | Orthogonal Multiwavelet Frames in L2Rd |
| title_sort | orthogonal multiwavelet frames in l2rd |
| url | http://dx.doi.org/10.1155/2012/846852 |
| work_keys_str_mv | AT liuzhanwei orthogonalmultiwaveletframesinl2rd AT huguoen orthogonalmultiwaveletframesinl2rd AT wuguochang orthogonalmultiwaveletframesinl2rd |