On dual wavelet tight frames

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 L-2(R) is generalized to the n-dimensional case. Two ways of constructing certain dual wavelet tight frames in L-2(R-n) are suggested. Finally, examples of smooth wavelet tight frames in L-2(R) and H-2(R) are provided. In particular, an example is given to demonstrate that there is a function psi whose Fourier transform is positive, compactly supported, and infinitely differentiable which generates a non-MRA wavelet tight frame in H-2(R). (C) 1997 Academic Press.