September  2007, 6(3): 741-756. doi: 10.3934/cpaa.2007.6.741

Reducing subspace frame multiresolution analysis and frame wavelets

1. 

Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, China

2. 

Department of Applied Mathematics, Beijing University of Technology, Beijing, 100022, China

Received  April 2006 Revised  March 2007 Published  June 2007

Multiresolution analysis (MRA) and frame multiresolution analysis (FMRA) in $L^2(\mathbb R)$ play a significant role in the construction of wavelets and frame wavelets for $L^2(\mathbb R)$. In this paper, the notions of MRA and FMRA in a reducing subspace of $L^2(\mathbb R)$ are introduced, from which the construction of wavelets and frame wavelets for this subspace is obtained. Many examples are also provided to illustrate the general theory. In particular, most of them are about the space with its frequency lying in $[0,\infty)$, which is closely related to various Paley-Wiener Theorems.
Citation: Qiao-Fang Lian, Yun-Zhang Li. Reducing subspace frame multiresolution analysis and frame wavelets. Communications on Pure & Applied Analysis, 2007, 6 (3) : 741-756. doi: 10.3934/cpaa.2007.6.741
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