Multipliers , Phases and Connectivity of Wavelets in L 2 ( R 2 )
Multipliers , Phases and Connectivity of Wavelets in L 2 ( R 2 )
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发表时间：
2008
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通讯作者：
Zhongyan Li
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作者：
Zhongyan Li
抽象的。设A是任意2 × 2真实的扩张矩阵.对于任何A-伸缩小波，设B是它的傅里叶变换。一个可测函数f称为A-伸缩小波乘子，如果（f B b）的逆傅里叶变换对任意A-伸缩小波都是A-伸缩小波.本文给出了所有A-伸缩小波乘子的一个完整刻画，条件是A是2×2整数元矩阵，|det（A）|= 2。利用这一结果，我们能够刻画A-伸缩小波的相位，并证明了对于任意A-伸缩矩阵，所有A-伸缩MRA小波的集合在L2（R2）范数拓扑下是路径连通的.
Abstract. Let A be any 2 × 2 real expansive matrix. For any A-dilation wavelet ψ, let b ψ be its Fourier transform. A measurable function f is called an A-dilation wavelet multiplier if the inverse Fourier transform of (f b ψ) is an Adilation wavelet for any A-dilation wavelet ψ. In this paper, we give a complete characterization of all A-dilation wavelet multipliers under the condition that A is a 2×2 matrix with integer entries and | det(A)| = 2. Using this result, we are able to characterize the phases of A-dilation wavelets and prove that the set of all A-dilation MRA wavelets is path-connected under the L2(R2) norm topology for any such matrix A.