ORDER OF LINEAR-APPROXIMATION FROM SHIFT-INVARIANT SPACES

A Fourier analysis approach is taken to investigate the approximation order of scaled versions of certain linear operators into shift-invari ant subspaces of L(2)(R(d)), Quasi-interpolants and cardinal interpola nts are special operators of this type, and we give a complete charact erization of the order in terms of some type of ellipticity condition for a related function. We apply these results by showing that the L(2 )-approximation order of a closed shift-invariant subspace can often h e realized by such an operator.