| Cascade algorithm and multiresolution analysis on the Heisenberg group |
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| 引用本文： | LIU Heping,LIU Yu,PENG Lizhong,CHU Xiaoyong. Cascade algorithm and multiresolution analysis on the Heisenberg group[J]. 自然科学进展(英文版), 2005, 15(7): 602-608. DOI: 10.1080/10020070512331342620 |
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| 作者姓名： | LIU Heping LIU Yu PENG Lizhong CHU Xiaoyong |
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| 作者单位： | LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China,LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China,LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China,LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China |
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| 基金项目： | Supported by National Natural Science Foundation of China (Grant Nos. 10371004, 10471002, and 90104004)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20030001107)the Major State Basic Research Development Program of China (Grant No. G1999075105) |
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| 摘 要： | In this paper we investigate the relationship between the convergence of cascade algorithm and orthogonal (or biorthogonal) multiresolution analysis on the Heisenberg group. It is proved that the (strong) convergence of cascade algorithm together with the perfect reconstruction condition induces an orthogonal multiresolution analysis and vice versa. Similar results are also proved for biorthogonal multiresolution analysis.
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| 关 键 词： | Heisenberg group cascade algorithm multiresolution analysis refinable functions. |
Cascade algorithm and multiresolution analysis on the Heisenberg group |
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| Liu Heping,LIU Yu,PENG Lizhong,CHU Xiaoyong. Cascade algorithm and multiresolution analysis on the Heisenberg group[J]. Progress in Natural Science, 2005, 15(7): 602-608. DOI: 10.1080/10020070512331342620 |
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| Authors: | Liu Heping LIU Yu PENG Lizhong CHU Xiaoyong |
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| Affiliation: | LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China |
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| Abstract: | In this paper we investigate the relationship between the convergence of cascade algorithm and orthogonal (or biorthogonal) multiresolution analysis on the Heisenberg group. It is proved that the (strong) convergence of cascade algorithm together with the perfect reconstruction condition induces an orthogonal multiresolution analysis and vice versa. Similar results are also proved for biorthogonal multiresolution analysis. |
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| Keywords: | Heisenberg group cascade algorithm multiresolution analysis refinable functions. |
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