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|Title:||Convergence of cascade algorithms and smoothness of refinable distributions|
Fractional sobolev space
Linear independent shifts
|Source:||Sun, Q. (2003). Convergence of cascade algorithms and smoothness of refinable distributions. Chinese Annals of Mathematics. Series B 24 (3) : 367-386. ScholarBank@NUS Repository. https://doi.org/10.1142/S0252959903000372|
|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 Hölder 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).|
|Source Title:||Chinese Annals of Mathematics. Series B|
|Appears in Collections:||Staff Publications|
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