Composition operators on the Wiener-Dirichlet algebra

Frédéric Bayart (1, 2) , Catherine Finet (3) , Daniel Li (4) , Hervé Queffélec (5)

1 IMB - Institut de Mathématiques de Bordeaux
2 LMBP - Laboratoire de Mathématiques Blaise Pascal
3 Institut de Mathématiques [Mons]
4 LML - Laboratoire de Mathématiques de Lens
5 LPP - Laboratoire Paul Painlevé - UMR 8524

We study the composition operators on an algebra of Dirichlet series, the analogue of the Wiener algebra of absolutely convergent Taylor series, which we call the Wiener-Dirichlet algebra. The central issue is to understand the connection between the properties of the operator and of its symbol, with special emphasis on the compact, automorphic, or isometric character of this operator. We are led to the intermediate study of algebras of functions of several, or countably many, complex variables.

Mots clés: composition operator; Dirichlet series

Domaines: Analyse fonctionnelle [math.FA]

Frédéric Bayart, Catherine Finet, Daniel Li, Hervé Queffélec. Composition operators on the Wiener-Dirichlet algebra. Journal of Operator Theory, 2008, 60 (1), pp.45 - 70. ⟨hal-00376140⟩