The canonical and alternate duals of a wavelet frame

被引：11
|
作者：
Bownik, Marcin [1 ]
Lemvig, Jakob
机构：
[1] Univ Oregon, Dept Math, Eugene, OR 97403 USA
[2] Tech Univ Denmark, Dept Math, DK-2800 Lyngby, Denmark
来源：
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS | 2007年 / 23卷 / 02期
关键词：
D O I：
10.1016/j.acha.2007.04.004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that there exists a frame wavelet psi with fast decay in the time domain and compact support in the frequency domain generating a wavelet system whose canonical dual frame cannot be generated by an arbitrary number of generators. On the other hand, there exists infinitely many alternate duals of psi generated by a single function. Our argument closes a gap in the original proof of this fact by Daubechies and Han [The canonical dual frame of a wavelet frame, Appl. Comput. Harmon. Anal. 12 (3) (2002) 269-2851. (c) 2007 Elsevier Inc. All rights reserved.
引用
收藏
页码：263 / 272
页数：10
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