On local and controlled approximation order (Q1801547)

The authors deal with approximations to smooth functions by objects which are essentially discrete convolutions. The purpose is to get error estimates for approximation power of dilates of these convolutions in terms of the dilation parameter \(h\). ``The authors have done it in this paper via well-known strange 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. This paper obtains a coherent theory for both these cases.