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We extend an uncertainty principle due to Beurling into a characterization of Hermite functions. More precisely, all functions f on R d which may be written as P (x) exp(Ax, x), with A a real symmetric definite positive matrix, are characterized by integrability conditions on the product f (x) f (y). We also give the best constant in uncertainty principles… (More)

Let {F n : n 1} be a normalized sequence of random variables in some fixed Wiener chaos associated with a general Gaussian field, and assume that

- Aline Bonami, Gustavo Garrig
- 2000

- ALINE BONAMI
- 2008

We prove that for all p > 1/2 there exists a constant γ p > 0 such that, for any symmetric measurable set of positive measure E ⊂ T and for any γ < γ p , there is an idempotent trigonometrical polynomial f satisfying E |f | p > γ T |f | p. This disproves a conjecture of Anderson, Ash, Jones, Rider and Saffari, who proved the existence of γ p > 0 for p > 1… (More)

We give a new proof and provide new bounds for the speed of convergence in the Central Limit Theorem of Breuer Major on stationary Gaussian time series, which generalizes to particular triangular arrays. Our assumptions are given in terms of the spectral density of the time series. We then consider generalized quadratic variations of Gaussian fields with… (More)

- ALINE BONAMI
- 2008

We say that Wiener's property holds for the exponent p > 0 if we have that whenever a positive definite function f belongs to L p (−ε, ε) for some ε > 0, then f necessarily belongs to L p (T), too. This holds true for p ∈ 2N by a classical result of Wiener. Recently various concentration results were proved for idempotents and positive definite functions on… (More)

- ALINE BONAMI, JUSTIN FEUTO
- 2007

We define as a distribution the product of a function (or distribution) h in some Hardy space H p with a function b in the dual space of H p. Moreover, we prove that the product b × h may be written as the sum of an integrable function with a distribution that belongs to some Hardy-Orlicz space, or to the same Hardy space H p , depending on the values of p.

- ALINE BONAMI
- 2009

This paper is dedicated to the memory of Andrzej Hulanicki who was a colleague, a friend we will never forget. Abstract. We study the holomorphic Hardy-Orlicz spaces H Φ (Ω), where Ω is the unit ball or, more generally, a convex domain of finite type or a strictly pseudoconvex domain in C n. The function Φ is in particular such that H 1 (Ω) ⊂ H Φ (Ω) ⊂ H p… (More)

- ALINE BONAMI, JUSTIN FEUTO
- 2009

We give a div-curl type lemma for the wedge product of closed differential forms on R n when they have coefficients respectively in a Hardy space and L ∞ or BM O. In this last case, the wedge product belongs to an appropriate Hardy-Orlicz space.