HELSON SETS, SPECTRAL SYNTHESIS AND APPLICATIONS TO OPERATORS

Brahim Bouya , Mohamed Zarrabi (1)

1 IMB - Institut de Mathématiques de Bordeaux

In this paper we highlight the role played by Helson sets and/or sets of spectral synthesis in some recent results in operator theory. We consider in particular the results on the cyclicity in L p spaces, the Katznelson-Tzafriri type theorems and polynomially bounded operators .

Domaines: Analyse fonctionnelle [math.FA]

Brahim Bouya, Mohamed Zarrabi. HELSON SETS, SPECTRAL SYNTHESIS AND APPLICATIONS TO OPERATORS. Harmonic analysis, function theory, operator theory, and their applications, 71–80, Theta Ser. Adv. Math., 19, Theta, Bucharest, 2017., 2015, Bordeaux, France. ⟨hal-02657265⟩