ON SOME PROPERTIES OF THE CLASS OF STATIONARY SETS

Pascal Lefèvre (1)

1 LML - Laboratoire de Mathématiques de Lens

Some new properties of the stationary sets (defined by G. Pisier in [12]) are studied. Some arithmetical conditions are given, leading to the non- stationarity of the prime numbers. It is shown that any stationary set is a set of continuity. Some examples of "large" stationary sets are given, which are not sets of uniform convergence.

Mots clés: UC sets; stationary sets; Sidon sets; sets of continuity; Rajchman sets; random Fourier series; Riesz products; UC sets.

Domaines: Analyse fonctionnelle [math.FA]

Pascal Lefèvre. ON SOME PROPERTIES OF THE CLASS OF STATIONARY SETS. Colloquium Mathematicum, 1998, 76 (1), pp.1-18. ⟨hal-00766023⟩