Multipliers for entire functions and an interpolation problem of Beurling
We characterize the interpolating sequences for the Bernstein space of entire functions of exponential type, in terms of a Beurling-type density condition and a Carleson-type separation condition. Our work extends a description previously given by Beurling in the case that the interpolating sequence...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 1999 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/164425 |
| Acceso en línea: | https://hdl.handle.net/2445/164425 |
| Access Level: | acceso abierto |
| Palabra clave: | Funcions de variables complexes Funcions enteres Functions of complex variables Entire functions |
| Sumario: | We characterize the interpolating sequences for the Bernstein space of entire functions of exponential type, in terms of a Beurling-type density condition and a Carleson-type separation condition. Our work extends a description previously given by Beurling in the case that the interpolating sequences are restricted to the real line. An essential role is played by a multiplier lemma, which permits us to link techniques from Hardy spaces with entire functions of exponential type. We finally present a characterization of the sampling sequences for the Bernstein space, also extending a density theorem of Beurling. |
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