| CONVERGENCE OF CASCADE ALGORITHMS AND SMOOTHNESS OF REFINABLE DISTRIBUTIONS |
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| 引用本文： | SUN Qiyu. CONVERGENCE OF CASCADE ALGORITHMS AND SMOOTHNESS OF REFINABLE DISTRIBUTIONS[J]. 数学年刊B辑(英文版), 2003, 24(3): 367-386 |
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| 作者姓名： | SUN Qiyu |
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| 作者单位： | SUN QIYU Department of Mathematics，University of Houston，Houston，TX 77204，USA. Department of Mathematics，National University of Singapore，10 Kent Ridge Crescent，119260，Singapore. |
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| 摘 要： | In this paper, the author at first develops a method to study convergence of the cascade algorithm in a Banach space without stable assumption on the initial (see Theorem 2.1), and then applies the previous result on the convergence to characterizing compactly supported refinable distributions in fractional Sobolev spaces and Holder continuous spaces (see Theorems 3.1, 3.3, and 3.4). Finally the author applies the above characterization to choosing appropriate initial to guarantee the convergence of the cascade algorithm (see Theorem 4.2).
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| 关 键 词： | 收敛性 级联法 光滑性 加细分布 Banach空间 移位不变空间 线性独立移位 稳定移位 分数 退火分布 Sobolev空间 |
| 收稿时间： | 2009-01-02 |
Convergence of Cascade Algorithms and Smoothness of Refinable Distributions |
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| SUN Qiyu. Convergence of Cascade Algorithms and Smoothness of Refinable Distributions[J]. Chinese Annals of Mathematics,Series B, 2003, 24(3): 367-386 |
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| Authors: | SUN Qiyu |
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| Affiliation: | Department of Mathematics, University of Houston,Houston,TX,77204,USA;Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, 119260, Singapore |
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| Abstract: | In this paper, the author at first develops a method to study convergence of the cascade algorithm in a Banach space without stable assumption on the initial (see Theorem 2.1), and then applies the previous result on the convergence to characterizing compactly supported refinable distributions in fractional Sobolev spaces and Holder continuous spaces (see Theorems 3.1, 3.3, and 3.4). Finally the author applies the above characterization to choosing appropriate initial to guarantee the convergence of the cascade algorithm (see Theorem 4.2). |
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| Keywords: | Cascade algorithm Cascade operator Refinable distribution Shift-invariant space Linear independent shifts Stable shifts Fractional Sobolev space |
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