Approximation orders of and approximation maps from local principal shift-invariant spaces
Let \(S\) be a shift-invariant subspace of \(L_p (\mathbb{R}^d)\), \(2\leq p\leq \infty\), which is generated by the shifts of one compactly supported function. In this paper the approximation order of \(S\) is considered by constructing explicit approximation maps. The approach avoids quasi-interpolation and applies to stationary and non-stationary refinements. The general results are specialized to box spline spaces, to obtain explicit approximation schemes that realize the approximation orders.
scientific article; zbMATH DE number 756641