Generalized Riesz Products on the Bohr compactification of $\R$

El Houcein El Abdalaoui (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

We study a class of generalized Riesz products connected to the spectral type of some class of rank one flows on $\R$. Applying a Central Limit Theorem of Kac, we exhibit a large class of singular generalized Riesz products on the Bohr compactification of $\R$. Moreover, we discuss the problem of the flat polynomials in this setting.

Mots clés: Generalized Riesz products; almost periodic functions; Bohr compactification; mean value; Besicovitch space; Kac Central Limit Theorem; Kakutani criterion; Kakutani criterion .

Domaines: Analyse classique [math.CA]

El Houcein El Abdalaoui. Generalized Riesz Products on the Bohr compactification of $\R$. 2012. ⟨hal-00703137v4⟩