Projectable multivariate refinable functions and biorthogonal wavelets.
In the paper, the concept of projectable refinable functions is introduced, and it is shown that many non\-separable multivariate refinable functions in the literature are projectable, i.e., they essentially carry the tensor product structure. Projected refinable functions are constructed via a special class of linear transforms. Further, its analysis (smoothness, approximation order) is given. The theory can be used to tackle the following problem: Given a refinable function \(\phi \in {\mathbb R}^{^s}\), what are the expected optimal upper bounds of the \(L_p\)-smoothness and approximation order of all the dual refinable functions \(\phi^d\) of \(\phi \) such that the support of \(\phi^d\) is contained in a fixed set \([-N, N]^s\)?
scientific article; zbMATH DE number 1891393