On Dual Wavelet Tight Frames

Abstract

A characterization of multivariate dual wavelet tight frames for any general dilation matrix is presented in this paper. As an application, Lawton's result on wavelet tight frames in L2(ℝ) is generalized to the n-dimensional case. Two ways of constructing certain dual wavelet tight frames in L2(ℝn) are suggested. Finally, examples of smooth wavelet tight frames in L2(ℝ) and H2(ℝ) are provided. In particular, an example is given to demonstrate that there is a function ψ whose Fourier transform is positive, compactly supported, and infinitely differentiable which generates a non-MRA wavelet tight frame in H2(ℝ). © 1997 Academic Press.