Hermite pseudospectral approximations. An error estimate

We find an error bound for the pseudospectral approximation of a function in terms of Hermite functions, hn(x) = e −x2 Hn(x), in certain weighted Sobolev spaces. We use properties of Hermite polynomials, as well as an asymptotic expression for their largest zeroes to achieve the mentioned estimate.  2004 Elsevier Inc. All rights reserved