Compression using quasi-interpolation

In this article we consider quasi-interpolation with a main application in radial basis functions approximations and compression. On constructing and using these quasi-interpolants, we consider wavelet and compression-type approximations from their linear spaces, and we provide convergence estimates. The results include an error estimate for nonlinear approximation by radial basis functions and quasi-interpolation, positive and negative results about compression in the space of continuous functions and a pointwise convergence estimate for approximands of low smoothness.