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This paper generalizes the mixed extension principle in L2(ℝd) of (Ron and Shen in J. Fourier Anal. Appl. 3:617–637, 1997) to a pair of dual Sobolev spaces Hs(ℝd) and H−s(ℝd). In terms of masks for φ,ψ1,…,ψL∈Hs(ℝd) and $\tilde{\phi},\tilde{\psi}^{1},\ldots,\tilde{\psi}^{L}\in H^{-s}({\mathbb{R}}^{d})$ , simple sufficient conditions are given to ensure that (Xs(φ;ψ1,…,...
Starting from any two compactly supported refinable functions in L2(R) with dilation factor d,we show that it is always possible to construct 2d wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L2(R). Moreover, the number of vanishing moments of each of these wavelet frames is equal to the approximation order of the dual MRA; this is the highest possible...
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