Reducing subspace frame multiresolution analysis and &nbsp;frame wavelets

Qiao-Fang Lian; Yun-Zhang Li

doi:10.3934/cpaa.2007.6.741

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2007, Volume 6, Issue 3: 741-756. Doi: 10.3934/cpaa.2007.6.741

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Reducing subspace frame multiresolution analysis and frame wavelets

Qiao-Fang Lian^1, and
Yun-Zhang Li^2,

1.
Department of Mathematics, Beijing Jiaotong University, Beijing, 100044
2.
Department of Applied Mathematics, Beijing University of Technology, Beijing, 100022

Received: April 2006

Revised: March 2007

Published: August 2007

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Abstract

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.

Keywords:

Subspace frame multiresolution analysis,
subspace frame wavelet,
reducing subspace.

Mathematics Subject Classification: 42C40.

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