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On dual wavelet tight frames. (English) Zbl 0880.42017
Summary: 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 $L^2(\bbfR)$ is generalized to the $n$-dimensional case. Two ways of constructing certain dual wavelet tight frames in $L^2(\bbfR^n)$ are suggested. Finally, examples of smooth wavelet tight frames in $L^2(\bbfR)$ and $H^2(\bbfR)$ 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 $H^2(\bbfR)$.

##### MSC:
 42C40 Wavelets and other special systems
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##### References:
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