Please use this identifier to cite or link to this item: https://doi.org/10.1142/S0252959903000372
Title: Convergence of cascade algorithms and smoothness of refinable distributions
Authors: Sun, Q. 
Keywords: Cascade algorithm
Cascade operator
Fractional sobolev space
Linear independent shifts
Refinable distribution
Shift-invariant space
Stable shifts
Issue Date: 2003
Citation: 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
URI: http://scholarbank.nus.edu.sg/handle/10635/103069
ISSN: 02529599
DOI: 10.1142/S0252959903000372
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