| ABSTRACT |
In this talk we consider almost everywhere convergence of the Bochner-Riesz means of the Hermite expansion and characterize the summability index for which the means converges almost everywhere. For $f\in L^p$ with $p\ge 2$ we show the Bochner-Riesz means converges almost everywhere if the summability index is bigger than $\alpha(p)=\max(n(1/4-1/2p)-1/4, 0)$ and the convergence generally fails if the index is smaller than $\alpha(p)$. This is in striking contrast with the classical Bochner-Riesz means of Fourier transform and Fourier series in that the required summability index is only half of the index for almost everywhere convergence of the classical Bochner-Riesz means of Fourier transform and Fourier series. |
