文献类型：期刊文献

英文题名：MRA PARSEVAL FRAME MULTIWAVELETS IN L-2(R-d)

作者：Liu, Zhanwei[1];Mu, Xiaomin[1];Wu, Guochang[2]

第一作者：Liu, Zhanwei

通讯作者：Liu, ZW[1]

机构：[1]Zhengzhou Univ, Sch Informat Engn, Zhengzhou 450001, Peoples R China;[2]Henan Univ Econ & Law, Dept Appl Math, Zhengzhou 450002, Peoples R China

第一机构：Zhengzhou Univ, Sch Informat Engn, Zhengzhou 450001, Peoples R China

通讯机构：[1]corresponding author), Zhengzhou Univ, Sch Informat Engn, Zhengzhou 450001, Peoples R China.

年份：2012

卷号：38

期号：4

起止页码：1021-1045

外文期刊名：BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000315561600013)】；

基金：The authors would like to express their gratitude to the referee for his (or her) valuable comments and suggestions that lead to a significant improvement of our manuscript. This work was supported by the Natural Science Foundation for the Education Department of Henan Province of China (No. 102300410205).

语种：英文

外文关键词：Frame; matrix filter; pseudo-scaling function; MRA Parseval frame multiwavelets; matrix multiwavelets multiplier

摘要：In this paper, we characterize multiresolution analysis (MRA) Parseval frame multiwavelets in L-2(R-d) with matrix dilations of the form (Df)(x) = root 2f(Ax), where A is an arbitrary expanding d x d matrix with integer coefficients, such that vertical bar detA vertical bar = 2. We study a class of generalized low pass matrix filters that allow us to define (and construct) the subclass of MRA tight frame multiwavelets. This leads us to an associated class of generalized scaling functions that are not necessarily obtained from a multiresolution analysis. We also investigate several properties of these classes of generalized multiwavelets, scaling functions, matrix filters and give some characterizations about them. Finally, we describe the matrix multipliers classes associated with Parseval frame multiwavelets (PFMWs) in L-2(R-d) and give an example to support our theory.