Oversampling, quasi-affine frames, and wave packets

被引：42
作者：
Hernández, E
Labate, D
Weiss, G [1 ]
Wilson, E
机构：
[1] Washington Univ, Dept Math, St Louis, MO 63130 USA
[2] Univ Autonoma Madrid, Madrid, Spain
来源：
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS | 2004年 / 16卷 / 02期
关键词：
affine systems; frames; Gabor systems; oversampling; quasi-affine systems; wavelets;
D O I：
10.1016/j.acha.2003.12.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In [E. Hernandez, D. Labate, G. Weiss, J. Geom. Anal. 12 (4) (2002) 615-662], three of the authors obtained a characterization of certain types of reproducing systems. In this work, we apply these results and methods to various affine-like, wave packets and Gabor systems to determine their frame properties. In particular, we study how oversampled systems inherit properties (like the frame bounds) of the original systems. Moreover, our approach allows us to study the phenomenon of oversampling in much greater generality than is found in the literature. (C) 2004 Elsevier Inc. All rights reserved.
引用
收藏
页码：111 / 147
页数：37
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