Abstract :
For any principal shift invariant space S(φ) generated by φ ∈ Wm2(Rs), a necessary and sufficient condition is supplied for determining whether S(φ) provides simultaneous approximation order (m, k). For a certain type of φ this necessary and sufficient condition is proved to be equivalent to having some constant const so that, for all β ∈ Zs\0, |φ̂(· + 2 πβ)| ≤ const |·|k |φ̂)| on a neighborhood of the origin.
