Composition operators in the Dirichlet series setting

• Autorzy: Hervé Queffélec
• Języki publikacji: EN

Abstrakty

EN

In this work, we begin with a survey of composition operators on the Hardy space H² and on the Wiener algebra A⁺ of absolutely convergent Taylor series, with special emphasis on their compactness, or invertibility, or isometric character. The main results are due respectively to J. Shapiro and D.~Newman. In a second part, we present more recent results, due to Gordon and Hedenmalm on the one hand, and to Bayart, the author et al. on the other hand, concerning the analogues of H² and A⁺ in the setting of Dirichlet series. We are led to the intermediate study of Taylor series in several, or countably many, variables. We finish with some open problems.

Kategorie tematyczne

• 42B35: Function spaces arising in harmonic analysis
• 30B50: Dirichlet series and other series expansions, exponential series
• 47B33: Composition operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2007
• Tom: 75
• Numer: 1
• Strony: 261-287

Daty

wydano

2007

Twórcy

autor

Hervé Queffélec

• U.F.R. de Mathématiques, Université de Lille 1, 59655 Villeneuve d'Ascq Cedex, France

Identyfikatory

DOI

10.4064/bc75-0-16