Multipliers, Phases and Connectivity of Wavelets in L²(R²)
by
Zhongyan Li
North China Electric Power University, Beijing, China
Coauthors: Xingde Dai, Yuanan Diao, Jianguo Xin(University of North Carolina at Charlotte)

Let A be any d×d real expansive matrix. For any A-dilation wavelet y, let [^(y)] be its Fourier transform. A measurable function f is called an A-dilation wavelet multiplier if the inverse Fourier transform of (f[^(y)]) is an A-dilation wavelet for any A-dilation wavelet y. In this paper, we consider the wavelet multiplier problem in the two dimensional case. 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 A-dilation MRA wavelets is path-connected under the L²(R²) norm topology for any such matrix A.

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Date received: February 16, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavq-52.