On random Hermite series

Rafik Imekraz (1) , Didier Robert (2) , Laurent Thomann (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Mots clés: Harmonic oscillator; harmonic analysis; random series; Hermite functions

Domaines: Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]; Analyse classique [math.CA]

Rafik Imekraz, Didier Robert, Laurent Thomann. On random Hermite series. Transactions of the American Mathematical Society, 2016, 368 (4), pp.2763--2792. ⟨hal-00961222⟩