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