$L^\infty$ boundedness of density for free additive convolutions

Serban Belinschi (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We show that the density of the free additive convolution of two Borel probability measures $\mu,\nu$ on $\mathbb R$ whose Cauchy transforms have reasonably good behaviour at infinity is bounded whenever $\mu(\{a\})+\nu(\{b\})<1$ for all $a,b\in\mathbb R$.

Mots clés: Free convolution; Analytic transforms; Regularity

Domaines: Algèbres d'opérateurs [math.OA]; Probabilités [math.PR]

Serban Belinschi. $L^\infty$ boundedness of density for free additive convolutions. Revue roumaine de mathématiques pures et appliquées, 2014, 59 (2), pp.173-184. ⟨hal-01012051⟩