On Local and Controlled Approximation Order Original Research Article

This paper deals with approximations to smooth functions by objects which are essentially discrete convolutions. The purpose is to get error estimates for the approximation power of dilates of these convolutions in terms of the dilation parameter h. The paper does this via the well-known Strang-Fix conditions, but there are some important modifications to previous treatments of this theory. In particular, the function used to generate the discrete convolution may or may not have compact support. The paper obtains a coherent theory for both these cases.