The \(n\)-variable Hermite polynomials are the polynomials orthogonal with respect to the Gaussian density \(\gamma(x)=\exp(-|x|^2)\). The author introduces weighted Sobolev spaces \(W^{2,s}(\gamma(x)dx)\) and shows that Hermite polynomial expansions on these spaces are uniformly convergent on compact sets for \(s>n/2\). The same is shown for weights which integrate \(\exp(\varepsilon|x|)\) for some \(\varepsilon>0\).
For the entire collection see [Zbl 0827.00021].