Cantor sets and cyclicity in weighted Dirichlet spaces

We treat the problem of characterizing the cyclic vectors in the weighted Dirichlet spaces, extending some of our earlier results in the classical Dirichlet space. The absence of a Carleson-type formula for weighted Dirichlet integrals necessitates the introduction of new techniques

Convergence of Lagrange interpolation series in the Fock spaces

We study the uniqueness sets, the weak interpolation sets, and convergence of the Lagrange interpolation series in radial weighted Fock spaces

Multiple sampling and interpolation in the classical Fock space

We study multiple sampling, interpolation and uniqueness for the classical Fock space in the case of unbounded mul-tiplicities

The Littlewood problem and non-harmonic Fourier series

In this paper, we give a direct quantitative estimate of $L^1$norms of non-harmonic trigonometric polynomials over large enough intervals. This extends the result by Konyagin and Mc Gehee, Pigno, Smith to the settingof trigonometric polynomials with non-integer frequencies.The result is a quantitative extension of a result by Nazarov and also covers a resultby Hudson and Leckband when the length of the interval goes to infinity.Comment: Tis version has been revised according to the referees remarks.The appendixes are not present in the final version, only in the arxiv/hal versio

Carleson measures and Oversampling in model spaces

The aim of this paper is to extend two results from the Paley--Wiener setting to more generalmodel spaces. The first one is an analogue of the oversampling Shannon sampling formula. The second one is a version of Donoho--Logan's Large Sieve Theorem which is a quantitative estimate of the embedding of the Paley--Wiener space into an $L^2(\R,\mu)$ space