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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)
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)