This article investigates the super-resolution phenomenon using the celebrated statistical estimator LASSO in the complex valued measure framework. More precisely, we study the recovery of a discrete measure (spike train) from few noisy observations (Fourier samples, moments, Stieltjes transformation...). In particular, we provide an explicit quantitative localization of the spikes. Moreover, o...

Let H be a separable infinite-dimensional Hubert space over R. The Fresnel class T(H) of H consists of all Fourier-Stieltjes transforms of bounded Borel measures on H. There are several results insuring that various functions of interest in connection with the Feynman integral and quantum mechanics are in 7{H). We give a theorem which has most of these results as corollaries as well as many fur...

We provide complete characterizations, on Banach spaces with cotype 2, of those linear operators which happen to be weakly mixing or strongly mixing transformations with respect to some nondegenerate Gaussian measure. These characterizations involve two families of small subsets of the circle: the countable sets, and the so-called sets of uniqueness for Fourier-Stieltjes series. The most intere...