SHIFT-INVARIANT SPACES ON THE REAL LINE

We investigate the structure of shift-invariant spaces generated by a finite number of compactly supported functions in L(p)(R) (1 less than or equal to p less than or equal to infinity). Based on a study of li near independence of the shifts of the;generators, we characterize suc h shift-invariant spaces in terms of the semi-convolutions of the gene rators with sequences on Z. Moreover, we show that such a shift;invari ant space provides L(p)-approximation order k if and only if it contai ns all polynomials of degree less than k.