Increasingly global convergence of Hermite serie
arXiv:2405.15917 · doi:10.1016/j.jmaa.2025.130360
Abstract
We study the convergence of the Hermite series of measurable functions on the real line. We characterize the norm convergence of truncated partial Hermite sums in rearrangement invariant spaces provided that the truncations vanish sufficiently slowly. Moreover, we provide the necessary and sufficient conditions for convergence in the Orlicz modular.
Accepted at Journal of Mathematical Analysis and Applications (JMAA)