A Paley-Wiener theorem for Bergman spaces with application to invariant subspaces

An analogue of the Paley–Wiener theorem is developed for weighted Bergman spaces of analytic functions in the upper half-plane. The result is applied to show that the invariant subspaces of the shift operator on the standard Bergman space of the unit disk can be identified with those of a convolutio...

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Detalles Bibliográficos
Autores: Duren, Peter, Gallardo Gutiérrez, Eva Antonia, Montes Rodríguez, Alfonso
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2007
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/48423
Acceso en línea:http://hdl.handle.net/11441/48423
https://doi.org/10.1112/blms/bdm026
Access Level:acceso abierto
Palabra clave:Bergman spaces
Paley-Wiener theorem
Fourier transform
Laguerre polynomials
Invariant subspaces
Bergman shift
Convolution operators
Volterra operators
Descripción
Sumario:An analogue of the Paley–Wiener theorem is developed for weighted Bergman spaces of analytic functions in the upper half-plane. The result is applied to show that the invariant subspaces of the shift operator on the standard Bergman space of the unit disk can be identified with those of a convolution Volterra operator on the space L2 (R+, (1/t)dt).