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...
| Autores: | , , |
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| 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 |
| 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). |
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