On random Hermite series

Imekraz, Rafik; Robert, Didier; Thomann, Laurent

doi:10.1090/tran/6607

On random Hermite series
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by Rafik Imekraz, Didier Robert and Laurent Thomann PDF

Trans. Amer. Math. Soc. 368 (2016), 2763-2792 Request permission

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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