Dyadic Bivariate Wavelet Multipliers in L^2（R@2）  

作　　者：Zhong Yan LI Xian Liang SHI 

机构地区：[1]College of Mathematics and Computer' Science, Hu'nan Normal University, Changsha 410081, P. R. China [2]Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2011年第8期1489-1500,共12页数学学报（英文版）

基　　金：Supported by NSFC （Grant Nos. 10671062 and 11071065）, Ph. D Programs Foundation of Ministry Education of China （Grant No. 20094306110004）; the first author !Ls also partially supported by the Project-sponsored by SRF for ROCS, SEM, the Fundamental Research Funds for the Central Universities, and China Postdoctoral Science Foundation funded project （Grant No. 20100480942）

摘　　要：The single 2 dilation wavelet multipliers in one-dimensional case and single A-dilation （where A is any expansive matrix with integer entries and [detA[ = 2） wavelet multipliers in twodimen- sional case were completely characterized by Wutam Consortium （1998） and Li Z., et al. （2010）. But there exist no results on multivariate wavelet multipliers corresponding to integer expansive dilation matrix with the absolute value of determinant not 2 in L^2（R^2）. In this paper, we choose 2I2 = （02 20 ） as the dilation matrix and consider the 212-dilation multivariate wavelet ψ = {ψ1, ψ2, ψ3 } （which is called a dyadic bivariate wavelet） multipliers. Here we call a measurable function family f ={fl, f2, f3} a dyadic bivariate wavelet multiplier if ψ1 = （F^-1（f1ψ1）,F^-1（f2ψ2）, F-l（f3ψ3）} is a dyadic bivariate wavelet for any dyadic bivariate wavelet ψ = {ψ1, ψ2, ψ3}, where f and F^- 1 denote the Fourier transform and the inverse transform of function f respectively. We study dyadic bivariate wavelet multipliers, and give some conditions for dyadic bivariate wavelet multipliers. We also give concrete forms of linear phases of dyadic MRA bivariate wavelets.The single 2 dilation wavelet multipliers in one-dimensional case and single A-dilation （where A is any expansive matrix with integer entries and [detA[ = 2） wavelet multipliers in twodimen- sional case were completely characterized by Wutam Consortium （1998） and Li Z., et al. （2010）. But there exist no results on multivariate wavelet multipliers corresponding to integer expansive dilation matrix with the absolute value of determinant not 2 in L^2（R^2）. In this paper, we choose 2I2 = （02 20 ） as the dilation matrix and consider the 212-dilation multivariate wavelet ψ = {ψ1, ψ2, ψ3 } （which is called a dyadic bivariate wavelet） multipliers. Here we call a measurable function family f ={fl, f2, f3} a dyadic bivariate wavelet multiplier if ψ1 = （F^-1（f1ψ1）,F^-1（f2ψ2）, F-l（f3ψ3）} is a dyadic bivariate wavelet for any dyadic bivariate wavelet ψ = {ψ1, ψ2, ψ3}, where f and F^- 1 denote the Fourier transform and the inverse transform of function f respectively. We study dyadic bivariate wavelet multipliers, and give some conditions for dyadic bivariate wavelet multipliers. We also give concrete forms of linear phases of dyadic MRA bivariate wavelets.

关 键 词：Dyadic bivariate wavelet dyadic bivariate wavelet multiplier dyadic MRA bivariate wavelet dyadic low pass filter Haar type dyadic wavelet 

分 类 号：O174.22[理学—数学] TP332.22[理学—基础数学]