Approximation from locally finite-dimensional shift-invariant spaces
Approximation from locally finite-dimensional shift-invariant spaces
After exploring some topological properties of locally finite-dimensional shift-invariant subspaces $S$ of $L_p(\mathbb {R}^s)$, we show that if $S$ provides approximation order $k$, then it provides the corresponding simultaneous approximation order. In the case $S$ is generated by a compactly supported function in $L_\infty (\mathbb {R})$, it is proved that …