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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 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)f̂(y). We also give the best constant in uncertainty principles of(More)
Let {Fn : n > 1} be a normalized sequence of random variables in some fixed Wiener chaos associated with a general Gaussian field, and assume that E[F 4 n ] → E[N] = 3, where N is a standard Gaussian random variable. Our main result is the following general bound: there exist two finite constants c, C > 0 such that, for n sufficiently large, c × max(|E[F 3(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)
We study the boundedness properties of truncation operators acting on bounded Hankel (or Toeplitz) infinite matrices. A relation with the Lacey-Thiele theorem on the bilinear Hilbert transform is established. We also study the behaviour of the truncation operators when restricted to Hankel matrices in the Schatten classes. 1. Statement of results In this(More)
The theory of compensated compactness initiated and developed by L. Tartar [Ta] and F. Murat [M] has been largely studied and extended to various setting. The famous paper of Coifman, Lions, Meyer and Semmes ( [CLMS]) gives an overview of this theory in the context of Hardy spaces in the Euclidean space R (n ≥ 1). They prove in particular, that, for n n+1 <(More)