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2014

On random Hermite series

Imekraz, Rafik, Robert, Didier, Thomann, Laurent

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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.

On random Hermite series · Around

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G. Szegö
1939
Earlier work this paper cites.
A. Erdélyi
1960
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R. Askey
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J.-P. Kahane
1968
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B. Muckenhoupt
1970
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B. Maurey
1976
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