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In this partly expository paper we study van der Corput sets in , with a focus on connections with harmonic analysis and recurrence properties of measure preserving dynamical systems. We prove multidimensional versions of some classical results obtained for d = 1 by Kamae and M. Mendès France and by Ruzsa, establish new characterizations, introduce and discuss some modifications of van der Corput sets which correspond to various notions of recurrence, provide numerous examples and formulate some...
Le théorème CRT dit comment reconstruire un signal à partir d’un échantillonnage de fréquences parcimonieux. L’hypothèse sur le signal, considéré comme porté par un groupe cyclique d’ordre , est qu’il est porté par un petit nombre de points, , et la méthode est de choisir aléatoirement fréquences et de minimiser dans l’algèbre de Wiener le prolongement à de la transformée de Fourier du signal réduite à ces fréquences. Quand est grand, la probabilité de reconstruire le signal est voisine...
The purposes of this paper may be described as follows:(i) to provide a useful substitute for the Cotlar-Stein lemma for Lp-spaces (the orthogonality conditions are replaced by certain fairly weak smoothness asumptions);(ii) to investigate the gap between the Hörmander multiplier theorem and the Littman-McCarthy-Rivière example - just how little regularity is really needed?(iii) to simplify and extend the work of Duoandikoetxea and Rubio de Francia and Christ and Stein, which sometimes has unnecessarily...
Vector-valued pseudo almost periodic functions are defined and their properties are investigated. The vector-valued functions contain many known functions as special cases. A unique decomposition theorem is given to show that a vector-valued pseudo almost periodic function is a sum of an almost periodic function and an ergodic perturbation.
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