Journal of Operator Theory

Volume 60, Issue 1, Summer 2008 pp. 45-70.

Composition operators on the Wiener-Dirichlet algebra

Authors: Frederic Bayart (1), Catherine Finet (2), Daniel Li (3), and Herve Queffelec (4)
Author institution: (1) Universite Bordeaux 1, 351 cours de la Liberation, 33405 Talence cedex, France
(2) Institut de Mathematique, Universite de Mons-Hainaut, ``Le Pentagone'', Avenue du Champ de Mars, 6, 7000 Mons, Belgique
(3) Laboratoire de Mathematiques de Lens EA 2462, Federation CNRS Nord-Pas-de-Calais FR 2956, Universite d'Artois, rue Jean Souvraz, SP18, 62307 Lens Cedex, France
(4) UFR de Mathematiques, Universite de Lille 1, 59655 Villeneuve d'Ascq Cedex, France

Summary: 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.

Keywords: Composition operator, Dirichlet series

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