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arXiv · 1403.4913

On random Hermite series

Rafik Imekraz·Didier Robert·Laurent Thomann
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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.

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Rafik Imekraz, Didier Robert, Laurent Thomann. 2014-03-19. On random Hermite series. https://arxiv.org/abs/1403.4913

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