Multipliers, Phases and Connectivity of MRA Wavelets in L-2(R-2)

作者：Li Zhongyan; Dai Xingde; Diao Yuanan^*; Xin Jianguo

来源：Journal of Fourier Analysis and Applications, 2010, 16(2): 155-176.

DOI：10.1007/s00041-009-9089-6

• Wavelet multipliers
• Phase of wavelet
• A-dilation MRA wavelets
• Connectivity of wavelets

Let A be any 2 x 2 real expansive matrix. For any A-dilation wavelet psi, let (psi) over cap be its Fourier transform. A measurable function f is called an A-dilation wavelet multiplier if the inverse Fourier transform of (f (psi) over cap) is an A-dilation wavelet for any A-dilation wavelet psi. In this paper, we give a complete characterization of all A-dilation wavelet multipliers under the condition that A is a 2 x 2 matrix with integer entries and vertical bar det(A)vertical bar = 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 L-2(R-2) norm topology for any such matrix A.

• 出版日期2010-4
• 单位华北电力大学