Quasi-interpolation with translates of a function having noncompact support

We establish a result related to a theorem of de Boor and Jia 1]. Their theorem, in turn, corrected and extended a result of Fix and Strang 5] concerning controlled approximation. In our result, the approximating functions are not required to have compact support, but satisfy instead conditions on their behavior at . Our theorem includes some recent results of Jackson 6] and is closely related to the work of Buhmann 2].Communicated by Carl de Boor