Maximal discrepancy for multiply generated shift-invariant spaces

被引：0
作者：
Hartmut Führ
Jun Xian
机构：
[1] RWTH Aachen University,Department of Mathematics and Guangdong Province Key Laboratory of Computational Science
[2] Sun Yat-sen University,undefined
来源：
Archiv der Mathematik | 2016年 / 106卷
关键词：
Shift-invariant spaces; Translation-invariance; Riesz generator; Commutator norm; 42C20; 94A20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we study multiply generated shift-invariant spaces V(Φ) and their invariance properties under arbitrary translations. We obtain a sufficient condition for a sharp estimate of shift-variance measure in multiply generated shift-invariant spaces, generalizing previous results from the singly generated orthonormal case to multiply generated Riesz systems. The sufficient condition is fulfilled under mild integrability and smoothness assumptions on the generators.
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页码：145 / 153
页数：8
相关论文
共 22 条
[1]  
Aach T.(2007)Comparative analysis of shift variance and cyclostationarity in multirate filter banks IEEE Trans. Circuits Syst., 54 1077-1087
[2]  
Aach T.(2009)On bounds for shift-variance in two-channel filter banks IEEE Trans. Signal. Processing. 57 4292-4303
[3]  
Führ H.(2010)Invariance of a shift-invariant space J. Four. Anal. Appl. 16 60-75
[4]  
Aldroubi A.(2004)Nonuniform average sampling and reconstruction in multiply generated shift-invariant spaces Constr. Approx., 20 173-189
[5]  
Aldroubi A.(2005)Convolution, average sampling, and a Calderon resolution of the identity for shift-invariant spaces J. Four. Anal. Appl 22 215-244
[6]  
Sun Q.(2011)Uncertainty principles and Balian-Low-type theorems in principal shift-invariant spaces Appl. Comp. Harm. Anal. 30 337-347
[7]  
Tang W. S.(2000)Translation invariance of orthogonal multiresolution analyses of Appl. Comput. Harmon. Anal. 9 128-145
[8]  
Aldroubi A.(2000)The structure of shift-invariant subspaces of J. Funct. Anal. 177 282-309
[9]  
Sun Q.(2014)Quantifying invariance properties of shift-invariant spaces Appl. Comput. Harmon. Anal. 36 516-521
[10]  
Tang W. S.(2009)Non-translation-invariance and the synchronization problem in wavelet sampling Acta Appl. Math. 107 373-398
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