On random Hermite series
Analysis of PDEs
2014-03-20 v1 Classical Analysis and ODEs
Spectral Theory
Abstract
We study integrability and continuity properties of random series of Hermite functions. We get optimal results which are analogues to classical results concerning Fourier series, like the Paley-Zygmund or the Salem-Zygmund theorems. We also consider the case of series of radial Hermite functions, which are not so well-behaved. In this context, we prove some L^p bounds of radial Hermite functions, which are optimal when p is large.
Cite
@article{arxiv.1403.4913,
title = {On random Hermite series},
author = {Rafik Imekraz and Didier Robert and Laurent Thomann},
journal= {arXiv preprint arXiv:1403.4913},
year = {2014}
}
Comments
33 pages