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| Convergence of Cascade Algorithms and Smoothness of Refinable Distributions |
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Citation： |
SUN Qiyu.Convergence of Cascade Algorithms and Smoothness of Refinable Distributions[J].Chinese Annals of Mathematics B,2003,24(3):367~386 |
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Net amount： 816 |
Authors： |
SUN Qiyu; |
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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). |
Keywords： |
Cascade algorithm, Cascade operator, Refinable distribution, Shift-invariant space, Linear independent shifts, Stable shifts, Fractional Sobolev space |
Classification： |
42C40, 42B35, 46E35 |
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